2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Morning Shift
| List-I | List-II |
|---|---|
| (a) MI of the rod (length L, Mass M, about an axis $ \bot $ to the rod passing through the midpoint) | (i) $8M{L^2}/3$ |
| (b) MI of the rod (length L, Mass 2M, about an axis $ \bot $ to the rod passing through one of its end) | (ii) $M{L^2}/3$ |
| (c) MI of the rod (length 2L, Mass M, about an axis $ \bot $ to the rod passing through its midpoint) | (iii) $M{L^2}/12$ |
| (d) MI of the rod (Length 2L, Mass 2M, about an axis $ \bot $ to the rod passing through one of its end) | (iv) $2M{L^2}/3$ |
Choose the correct answer from the options given below:
A.
(a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)
B.
(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
C.
(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
D.
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 27th July Morning Shift
The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is $ \bot $ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)
A.
R2 : r2
B.
2r4 : R4
C.
2R2 : r2
D.
2R4 : r4
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 25th July Morning Shift
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be Ix, Iy and Iz respectively. The respectively radii of gyration about all the three axes will be the same.
Reason R : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :
Assertion A : Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be Ix, Iy and Iz respectively. The respectively radii of gyration about all the three axes will be the same.
Reason R : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :
A.
Both A and R are correct but R is NOT the correct explanation of A.
B.
A is not correct but R is correct.
C.
A is correct but R is not correct.
D.
Both A and R are correct and R is the correct explanation of A.
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 22th July Evening Shift
Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.
The correct statement for this situation is
The correct statement for this situation is
A.
All of them will have same velocity.
B.
The ring has greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.
C.
The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.
D.
The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 20th July Evening Shift
A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :
A.
Solid sphere
B.
Solid cylinder
C.
Hollow cylinder
D.
Ring
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Evening Shift
Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the center is :
A.
${1 \over 4}{{M{L^2}} \over {{\pi ^2}}}$
B.
${1 \over 2}{{M{L^2}} \over {{\pi ^2}}}$
C.
${2 \over 5}{{M{L^2}} \over {{\pi ^2}}}$
D.
${{M{L^2}} \over {{\pi ^2}}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Evening Shift
A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is :
[The coefficient of static friction, $\mu$s' is 0.4]
[The coefficient of static friction, $\mu$s' is 0.4]
A.
0
B.
5 mg
C.
${7 \over 2}$ mg
D.
${{mg} \over 5}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 18th March Morning Shift
A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $\omega$. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become :
A.
$\omega {M \over {M + m}}$
B.
$\omega {{M + 2m} \over M}$
C.
$\omega {M \over {M + 2m}}$
D.
$\omega {{M - 2m} \over {M + 2m}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 17th March Evening Shift
A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30$^\circ$ with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?
A.
0.60 s
B.
0.52 s
C.
0.80 s
D.
0.57 s
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 17th March Morning Shift
A triangular plate is shown. A force $\overrightarrow F $ = 4$\widehat i$ $-$ 3$\widehat j$ is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :
A.
$-$ 15 + 20$\sqrt 3 $, 15 + 20$\sqrt 3 $
B.
15 $-$ 20$\sqrt 3 $, 15 + 20$\sqrt 3 $
C.
15 + 20$\sqrt 3 $, 15 $-$ 20$\sqrt 3 $
D.
$-$ 15 $-$ 20$\sqrt 3 $, 15 $-$ 20$\sqrt 3 $
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 17th March Morning Shift
A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $\omega$. The angular momentum of M about point A is LA which lies in the positive z direction and the angular momentum of M about point B is LB. The correct statement for this system is :
A.
LA is constant, both in magnitude and direction
B.
LB is constant in direction with varying magnitude
C.
LB is constant, both in magnitude and direction
D.
LA and LB are both constant in magnitude and direction
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th February Evening Shift
A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be :
A.
${{2mgh} \over {I + 2m{r^2}}}$
B.
${{2mgh} \over {I + m{r^2}}}$
C.
2gh
D.
${{2gh} \over {I + m{r^2}}}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 26th February Morning Shift
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
A.
${4 \over 5}m{a^2}$
B.
${8 \over 5}m{a^2} + m{b^2}$
C.
${4 \over 5}m{a^2} + 2m{b^2}$
D.
${8 \over 5}m{a^2} + 2m{b^2}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 25th February Evening Shift
A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?
A.
${{v_0^2} \over {2g\sin \theta }}$
B.
${{7v_0^2} \over {10g\sin \theta }}$
C.
${2 \over 5}{{v_0^2} \over {g\sin \theta }}$
D.
${{v_0^2} \over {5g\sin \theta }}$
2021
JEE Mains
MCQ
JEE Main 2021 (Online) 24th February Morning Shift
Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as;
I1 = M.I. of thin circular ring about its diameter,
I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,
I3 = M.I. of solid cylinder about its axis and
I4 = M.I. of solid sphere about its diameter.
Then :
I1 = M.I. of thin circular ring about its diameter,
I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,
I3 = M.I. of solid cylinder about its axis and
I4 = M.I. of solid sphere about its diameter.
Then :
A.
I1 = I2 = I3 > I4
B.
I1 + I3 < I2 + I4
C.
I1 = I2 = I3 < I4
D.
I1 + I2 = I3 + ${5 \over 2}$ I4
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Evening Slot
The linear mass density of a thin rod AB of length L varies from A to B as
$\lambda \left( x \right) = {\lambda _0}\left( {1 + {x \over L}} \right)$, where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :
$\lambda \left( x \right) = {\lambda _0}\left( {1 + {x \over L}} \right)$, where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is :
A.
${2 \over 5}M{L^2}$
B.
${5 \over {12}}M{L^2}$
C.
${7 \over {18}}M{L^2}$
D.
${3 \over 7}M{L^2}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Morning Slot
Four point masses, each of mass m, are fixed at the corners of a square of side $l$. The square is
rotating with angular frequency $\omega $, about an axis passing through one of the corners of the square
and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this
axis is :
A.
3m$l$2$\omega $
B.
4m$l$2$\omega $
C.
m$l$2$\omega $
D.
2m$l$2$\omega $
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Morning Slot
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its
top, R and height, H, then its moment of inertia about its axis is :
A.
${{M\left( {{R^2} + {H^2}} \right)} \over 3}$
B.
${{M{R^2}} \over 2}$
C.
${{M{R^2}} \over 3}$
D.
${{M{H^2}} \over 3}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Evening Slot
A ring is hung on a nail. It can oscillate, without
slipping or sliding
(i) in its plane with a time period T1 and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T2. The ratio ${{{T_1}} \over {{T_2}}}$ will be :
(i) in its plane with a time period T1 and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T2. The ratio ${{{T_1}} \over {{T_2}}}$ will be :
A.
${{\sqrt 2 } \over 3}$
B.
${2 \over {\sqrt 3 }}$
C.
${2 \over 3}$
D.
${3 \over {\sqrt 2 }}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Morning Slot
A wheel is rotating freely with an angular speed
$\omega $ on a shaft. The moment of inertia of the
wheel is I and the moment of inertia of the
shaft is negligible. Another wheel of moment of
inertia 3I initially at rest is suddenly coupled to
the same shaft. The resultant fractional loss in
the kinetic energy of the system is :
A.
0
B.
${5 \over 6}$
C.
${1 \over 4}$
D.
${3 \over 4}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes
perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is :
A.
${1 \over 2}$
B.
${1 \over 4}$
C.
${1 \over 8}$
D.
${2 \over 3}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
Consider two uniform discs of the same thickness and different radii R1
= R and
R2 = $\alpha $R made of the same material. If the ratio of their moments of inertia I1 and I2 , respectively, about their axes is I1 : I2 = 1 : 16 then the value of $\alpha $ is :
R2 = $\alpha $R made of the same material. If the ratio of their moments of inertia I1 and I2 , respectively, about their axes is I1 : I2 = 1 : 16 then the value of $\alpha $ is :
A.
$\sqrt 2 $
B.
2
C.
$2\sqrt 2 $
D.
4
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
A uniform rod of length ‘$l$’ is pivoted at one of its ends on a vertical shaft of negligible radius.
When the shaft rotates at angular speed $\omega $ the rod makes an angle $\theta $ with it (see figure). To find $\theta $
equate the rate of change of angular momentum (direction going into the paper) ${{m{l^2}} \over {12}}{\omega ^2}\sin \theta \cos \theta $
about the centre of mass (CM) to the torque provided by the horizontal and vertical forces FH
and
FV
about the CM. The value of $\theta $ is then such that :
A.
$\cos \theta = {{2g} \over {3l{\omega ^2}}}$
B.
$\cos \theta = {{3g} \over {2l{\omega ^2}}}$
C.
$\cos \theta = {g \over {2l{\omega ^2}}}$
D.
$\cos \theta = {g \over {l{\omega ^2}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Morning Slot
Moment of inertia of a cylinder of mass M,
length L and radius R about an axis passing
through its centre and perpendicular to the
axis of the cylinder is
I = $M\left( {{{{R^2}} \over 4} + {{{L^2}} \over {12}}} \right)$. If such a cylinder is to be made for a given mass of a material, the ratio ${L \over R}$ for it to have minimum possible I is
I = $M\left( {{{{R^2}} \over 4} + {{{L^2}} \over {12}}} \right)$. If such a cylinder is to be made for a given mass of a material, the ratio ${L \over R}$ for it to have minimum possible I is
A.
${3 \over 2}$
B.
$\sqrt {{3 \over 2}} $
C.
$\sqrt {{2 \over 3}} $
D.
${{2 \over 3}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Evening Slot
Two uniform circular discs are rotating
independently in the same direction around
their common axis passing through their
centres. The moment of inertia and angular
velocity of the first disc are 0.1 kg-m2 and 10
rad s–1 respectively while those for the second
one are 0.2 kg-m2 and 5 rad s–1 respectively. At
some instant they get stuck together and start
rotating as a single system about their common
axis with some angular speed. The kinetic
energy of the combined system is :
A.
${{20} \over 3}J$
B.
${{5} \over 3}J$
C.
${{10} \over 3}J$
D.
${{2} \over 3}J$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Morning Slot
A uniform cylinder of mass M and radius R is to
be pulled over a step of height a (a < R) by
applying a force F at its centre ‘O’
perpendicular to the plane through the axes of
the cylinder on the edge of the step (see
figure). The minimum value of F required is :
A.
$Mg\sqrt {1 - {{\left( {{{R - a} \over R}} \right)}^2}} $
B.
$Mg\sqrt {1 - {{{a^2}} \over {{R^2}}}} $
C.
$Mg{a \over R}$
D.
$Mg\sqrt {{{\left( {{R \over {R - a}}} \right)}^2} - 1} $
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 2nd September Morning Slot
Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is :
A.
0.5 mg
B.
2 mg
C.
0.75 mg
D.
1 mg
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Evening Slot
A uniformly thick wheel with moment of inertia
I and radius R is free to rotate about its centre
of mass (see fig). A massless string is wrapped
over its rim and two blocks of masses m1 and
m2 (m1 $ > $ m2) are attached to the ends of the
string. The system is released from rest. The
angular speed of the wheel when m1 descents
by a distance h is :
A.
${\left[ {{{2\left( {{m_1} + {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$
B.
${\left[ {{{{m_1} + {m_2}} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$
C.
${\left[ {{{\left( {{m_1} - {m_2}} \right)} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$
D.
${\left[ {{{2\left( {{m_1} - {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Morning Slot
Three solid spheres each of mass m and
diameter d are stuck together such that the lines
connecting the centres form an equilateral
triangle of side of length d. The ratio I0/IA of
moment of inertia I0 of the system about an axis
passing the centroid and about center of any
of the spheres IA and perpendicular to the plane
of the triangle is :
A.
${{13} \over {23}}$
B.
${{23} \over {13}}$
C.
${{15} \over {13}}$
D.
${{13} \over {15}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Evening Slot
A uniform sphere of mass 500 g rolls without
slipping on a plane horizontal surface with its
centre moving at a speed of 5.00 cm/s. Its
kinetic energy is :
A.
8.75 × 10–3 J
B.
1.13 × 10–3 J
C.
8.75 × 10–4 J
D.
6.25 × 10–4 J
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 8th January Morning Slot
Consider a uniform rod of mass M = 4m and
length $\ell $ pivoted about its centre. A mass m
moving with velocity v making angle $\theta = {\pi \over 4}$ to
the rod's long axis collides with one end of the
rod and sticks to it. The angular speed of the
rod-mass system just after the collision is :
A.
${{3\sqrt 2 } \over 7}{v \over \ell }$
B.
${3 \over 7}{v \over \ell }$
C.
${3 \over {7\sqrt 2 }}{v \over \ell }$
D.
${4 \over 7}{v \over \ell }$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Evening Slot
Mass per unit area of a circular disc of radius $a$ depends on the distance r from its centre as $\sigma \left( r \right)$ = A + Br
. The moment of inertia of the disc about the axis, perpendicular to the plane and
assing through its centre is:
A.
$2\pi {a^4}\left( {{A \over 4} + {{aB} \over 5}} \right)$
B.
$\pi {a^4}\left( {{A \over 4} + {{aB} \over 5}} \right)$
C.
$2\pi {a^4}\left( {{{aA} \over 4} + {B \over 5}} \right)$
D.
$2\pi {a^4}\left( {{A \over 4} + {B \over 5}} \right)$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Morning Slot
The radius of gyration of a uniform rod of length $l$, about an axis passing through a
point ${l \over 4}$ away from the centre of the rod,
and perpendicular to it, is :
A.
${1 \over 8}l$
B.
${1 \over 4}l$
C.
$\sqrt {{7 \over {48}}} l$
D.
$\sqrt {{3 \over 8}} l$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Morning Slot
As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:
A.
$r\sqrt {{3 \over {2gh}}} $
B.
$r\sqrt {{3 \over {4gh}}} $
C.
${1 \over r}\sqrt {{{4gh} \over 3}} $
D.
${1 \over r}\sqrt {{{2gh} \over 3}} $
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
A uniform rod of length $\ell $ is being rotated in a horizontal plane with a constant angular speed about an axis
passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from
the axis, then which of the following graphs depicts it most closely?
A.
B.
C.
D.
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc
varies as $\left( {{{{\sigma _0}} \over r}} \right)$
, then the radius of gyration of the disc about its axis passing through the centre is:
A.
$\sqrt {{{{a^2} + {b^2} + ab} \over 2}} $
B.
$\sqrt {{{a + b} \over 3}} $
C.
$\sqrt {{{{a^2} + {b^2} + ab} \over 3}} $
D.
$\sqrt {{{a + b} \over 2}} $
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Morning Slot
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $\theta $0. If the
person stands up when the swing passes through its lowest point, the work done by him, assuming that his
center of mass moves by a distance $\ell $($\ell $ << L), is close to;
A.
mg$\ell $(1 + $\theta $02)
B.
mg$\ell $
C.
mg$\ell $(1 + ${{\theta _0^2} \over 2}$)
D.
mg$\ell $(1 - $\theta $02)
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
The time dependence of the position of a particle of mass m = 2 is given by $\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$
. Its angular
momentum, with respect to the origin, at time t = 2 is
A.
36 $\widehat k$
B.
- 48 $\widehat k$
C.
$ - 34\left( {\widehat k - \widehat i} \right)$
D.
$48\left( {\widehat i + \widehat j} \right)$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the
figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25
rotations per second in 5s, is close to :
A.
7.9 × 10–6 Nm
B.
4.0 × 10–6 Nm
C.
2.0 × 10–5 Nm
D.
1.6 × 10–5 Nm
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of ${{7M} \over 8}$
and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere.
Let I1 be the moment of inertia of the disc about its axis and I2 be the moment of inertia of the new sphere
about its axis. The ratio I1/I2 is given by :
A.
65
B.
140
C.
185
D.
285
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
Two coaxial discs, having moments of inertia
I1 and I1/2, are rotating with respective angular
velocities $\omega $1 and
$\omega $1/2
, about their common axis.
They are brought in contact with each other and
thereafter they rotate with a common angular
velocity. If Ef and Ei are the final and initial total
energies, then (Ef - Ei) is:
A.
${{{I_1}\omega _1^2} \over {24}}$
B.
${{{I_1}\omega _1^2} \over {12}}$
C.
${3 \over 8}{I_1}\omega _1^2$
D.
${{{I_1}\omega _1^2} \over {6}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
A particle of mass m is moving along a
trajectory given by
x = x0 + a cos$\omega $1t
y = y0 + b sin$\omega $2t
The torque, acting on the particle about the origin, at t = 0 is :
x = x0 + a cos$\omega $1t
y = y0 + b sin$\omega $2t
The torque, acting on the particle about the origin, at t = 0 is :
A.
Zero
B.
+my0a $\omega _1^2$$\widehat k$
C.
$ - m\left( {{x_0}b\omega _2^2 - {y_0}a\omega _1^2} \right)\widehat k$
D.
m (–x0b + y0a) $\omega _1^2$$\widehat k$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
A thin disc of mass M and radius R has mass
per unit area $\sigma $(r) = kr2 where r is the distance
from its centre. Its moment of inertia about an
axis going through its centre of mass and
perpendicular to its plane is :
A.
${{M{R^2}} \over 3}$
B.
${{M{R^2}} \over 6}$
C.
${{2M{R^2}} \over 3}$
D.
${{M{R^2}} \over 2}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
A thin smooth rod of length L and mass M is
rotating freely with angular speed $\omega $0 about an
axis perpendicular to the rod and passing
through its center. Two beads of mass m and
negligible size are at the center of the rod
initially. The beads are free to slide along the
rod. The angular speed of the system , when
the beads reach the opposite ends of the rod,
will be :-
A.
${{M{\omega _0}} \over {M + 3m}}$
B.
${{M{\omega _0}} \over {M + m}}$
C.
${{M{\omega _0}} \over {M + 6m}}$
D.
${{M{\omega _0}} \over {M + 2m}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Evening Slot
Moment of inertia of a body about a given axis
is 1.5 kg m2. Initially the body is at rest. In order
to produce a rotational kinetic energy of
1200 J, the angular accleration of 20 rad/s2
must be applied about the axis for a
duration of :-
A.
2.5 s
B.
3 s
C.
5s
D.
2 s
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
The following bodies are made to roll up
(without slipping) the same inclined plane from
a horizontal plane. : (i) a ring of radius R, (ii)
a solid cylinder of radius
R/2 and (iii) a solid
sphere of radius
R/4 . If in each case, the speed
of the centre of mass at the bottom of the incline
is same, the ratio of the maximum heights they
climb is :
A.
20 : 15 : 14
B.
4 : 3 : 2
C.
2 : 3 : 4
D.
10 : 15 : 7
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it,
its kinetic energy as a function of $\theta $, where $\theta $
is the angle by which it has rotated, is given as
k$\theta $2. If its moment of inertia is I then the
angular acceleration of the disc is :
A.
${k \over {4I}}\theta $
B.
${k \over {I}}\theta $
C.
${k \over {2I}}\theta $
D.
${2k \over {I}}\theta $
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
A rectangular solid box of length 0.3 m is held
horizontally, with one of its sides on the edge
of a platform of height 5m. When released, it
slips off the table in a very short time t = 0.01s,
remaining essentially horizontal. The angle by
which it would rotate when it hits the ground
will be (in radians) close to :-
A.
0.28
B.
0.02
C.
0.3
D.
0.5
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
A solid sphere and solid cylinder of identical
radii approach an incline with the same linear
velocity (see figure). Both roll without slipping
all throughout. The two climb maximum
heights hsph and hcyl on the incline. The ratio
hsph/hcyl is given by :-
A.
1
B.
14/15
C.
4/5
D.
2/$\sqrt5$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Evening Slot
An electric dipole is formed by two equal and
opposite charges q with separation d. The
charges have same mass m. It is kept in a
uniform electric field E. If it is slightly rotated
from its equilibrium orientation, then its angular
frequency $\omega$ is :-
A.
$\sqrt {{{qE} \over {md}}} $
B.
$\sqrt {{{qE} \over {2md}}} $
C.
$\sqrt {{{qE} \over {-2md}}} $
D.
$\sqrt {{{2qE} \over {md}}} $
Moment of inertia