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968 Questions Start Allen Test
All Exams Allen Advance Errorless
Q651 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the arrangement shown, the wedge of mass $M$ moves towards left with an acceleration $a$ . All surfaces are smooth. The acceleration of mass $m$ relative to wedge is
A.
$\frac{a}{2}$
B.
$\frac{2Ma}{m}$
C.
$\frac{2(M + m)a}{m}$
D.
$\frac{(M + m)a}{m}$
Q652 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body $A$ rests on $B$ and friction coefficient between $A$ and $B$ is $\mu$ . Block $M$ is placed on a frictionless surface. Then (i) (ii)
A.
the maximum possible value of $F$ so that both bodies move together in case (i) is $\mu(m+M)g$
B.
the maximum possible value of F so that both bodies move together in case (i) is $\mu mg$
C.
the maximum possible value of $F$ so that both bodies move together in case (ii) is $\mu(M+m)g$
D.
the maximum possible value of $F$ so that both bodies move together in case (ii) is $\mu Mg$
Q653 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A bicycle is in motion. When it is not pedalled, the force of friction exerted by the ground on two wheels is such that it acts
A.
in the backward direction on the front wheel and in the forward direction on the rear wheel
B.
in the forward direction on the front wheel and in the backward direction on rear wheel
C.
in the backward direction on both the front and the rear wheels
D.
in the forward direction on both the front and the rear wheels
Q654 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is moving in a circular path and its acceleration vector is making an angle of $30^{\circ}$ with the velocity vector, then the ratio of centripetal acceleration to its tangential acceleration is
A.
$\frac{1}{2}$
B.
$\frac{\sqrt{3}}{2}$
C.
$\frac{1}{\sqrt{3}}$
D.
$\sqrt{3}$
Q655 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is moving is x-y plane as shown in a circular path of radius 2 m. At a certain instant when the body is crossing the positive y-axis its acceleration is $(6\hat{i}-8\hat{j})\mathrm{ms}^{-2}$ . Then its angular acceleration and angular velocity at this instant will be
A.
$-3\hat{k}$ rads $^{-2}$ and $-2\hat{k}$ rads $^{-1}$ respectively
B.
$+3\hat{k}$ rads $^{-2}$ and $+2\hat{k}$ rads $^{-1}$ respectively
C.
$-4\hat{k}$ rads $^{-2}$ and $-\sqrt{3}\hat{k}$ rads $^{-1}$ respectively
D.
$+4\hat{k}$ rads $^{-2}$ and $+\sqrt{3}\hat{k}$ rads $^{-1}$ respectively
Q656 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block of mass m is attached to an ideal spring and system lies in vertical plane as shown. Initially the supporting plane is placed so that spring remains in its natural length then the plane is moved very slowly downwards. The graph showing variation of normal reaction applied by mass on supporting plane with distance travelled by block is
A.
B.
C.
D.
None of these
Q657 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two identical heavy spheres of equal mass are placed on smooth cup of radius $3r$ , where $r$ is radius of each sphere as shown. Then the ratio of reaction force between cup and any sphere to reaction force between two sphere is
A.
1
B.
2
C.
3
D.
None of these
Q658 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the given figure, the coefficient of friction between $m_{1}$ and $m_{2}$ is $\mu$ and $m_{2}$ and horizontal surface is zero
A.
If $F > \mu m_1g$ , then relative acceleration is found between $m_1$ and $m_2$
B.
If $F < \mu m_1g$ , then no relative acceleration is found between $m_1$ and $m_2$
C.
If $F > \mu m_{1}g$ , then both bodies move together
D.
A and B are correct
Q659 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is $\mu$ . The inclination $\theta$ of the plane is
A.
$\tan^{-1}(\mu)$
B.
$\tan^{-1}\left(\frac{\mu}{2}\right)$
C.
$\tan^{-1}(2\mu)$
D.
$\tan^{-1}(3\mu)$
Q660 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A circular tube of radius R and cross-sectional radius $r(r \ll R)$ is filled completely with iron balls of radius $\rho$ . Iron balls are just fitting into the tubes. The tension in the tube when it is rotated about its axis perpendicular to its plane with angular velocity $\omega$ is
A.
$\frac{4}{3}\pi\rho\omega^{2}r^{3}R$
B.
$\frac{4}{3}\pi\rho\omega^{2}r^{2}R^{2}$
C.
$\frac{2}{3}\pi\rho\omega^{2}r^{3}R$
D.
$\frac{2}{3}\pi\rho\omega^{2}r^{2}R^{2}$
Q661 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A plumb-line is set up on a rotating disk and makes an angle of $\alpha$ with the vertical, as in figure. The distance $r$ from the point of suspension to the axis of rotation is known, and so is the length $l$ of the thread. The angular velocity of rotation is
A.
$\omega = \sqrt{\frac{g\tan\alpha}{r + l\sin\alpha}}$
B.
$\omega = \sqrt{\frac{g\sin\alpha}{r + l\tan\alpha}}$
C.
$\omega = \sqrt{\frac{g}{r + l\sin\alpha}}$
D.
$\omega = \sqrt{\frac{g\cos\alpha}{r + l\sin\alpha}}$
Q662 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The force exerted by the ideal string on the ideal pulley $P$ is
A.
mg
B.
2mg
C.
$\sqrt{2}mg$
D.
4mg
Q663 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A rope of mass $M$ is hanged from two supports $A$ and $B$ as shown in figure. Maximum and minimum tension in the rope respectively are
A.
$\frac{Mg\cos\theta_2}{\sin(\theta_1 + \theta_2)},\frac{Mg\cos\theta_1}{\sin(\theta_1 + \theta_2)}$
B.
Mg, $Mg\cos\theta_{1}$
C.
$\frac{Mg\cos\theta_{2}}{\sin\left(\theta_{1}+\theta_{2}\right)}$ , $\frac{Mg\cos\theta_{1}\cos\theta_{2}}{\sin\left(\theta_{1}+\theta_{2}\right)}$
D.
$\frac{Mg\cos\theta_{2}}{\cos(\theta_{2}-\theta_{1})}$ , $\frac{Mg\cos\theta_{1}}{\sin(\theta_{1}+\theta_{2})}$
Q664 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Three blocks are arranged as shown in which ABCD is a horizontal plane. Strings are massless and both pulley stands vertical while the strings connecting blocks $m_{1}$ and $m_{2}$ are also vertical and are perpendicular to faces AB and BC which are mutually perpendicular to each other. If $m_{1}$ and $m_{2}$ are 3 kg and 4 kg respectively. Coefficient of friction between the block $m_{3}=10$ kg and surface is $\mu=0.6$ , then, frictional force on $m_{3}$ is
A.
$30\mathrm{N}$
B.
$40\mathrm{N}$
C.
$50\mathrm{N}$
D.
$60\mathrm{N}$
Q665 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block $A$ is placed over a long rough plank $B$ of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time $t = 0$ , block $A$ is given a velocity $v_{0}$ in horizontal direction. Let $v_{1}$ and $v_{2}$ be the velocities of $A$ and $B$ at time $t$ . Then choose the correct graph between $v_{1}$ or $v_{2}$ and $t$
A.
B.
C.
$$<br /> v _ {1} \text { or } v _ {2}<br /> $$
D.
$v_{1}$ or $v_{2}$
Q666 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Which of the following correctly describes the centripetal acceleration vector for a particle moving in a circular path?
A.
Constant and always perpendicular to the velocity vector for the particle
B.
Constant and always parallel to the velocity vector for the particle
C.
Of constant magnitude and always perpendicular to the velocity for the particle
D.
Of constant magnitude and always parallel to the velocity vector for the particle
Q667 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{\pi}$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is
A.
ML
B.
2ML
C.
4ML
D.
16ML
Q668 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block of mass m is slipping down a rough inclined wedge kept at rest on a horizontal table, with constant velocity. Force on wedge by the table is
A.
less than $(m+M)g$
B.
equal to $(m+M)g$
C.
equal to $\left(M + m\cos^2\theta\right)g$
D.
will make some non-zero angle with vertical direction
Q669 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
All surface are frictionless and pulley and strings are light. Acceleration of block of mass m is
A.
$\frac{2}{5}g$
B.
$\frac{4g}{5}$
C.
$\frac{4g}{7}$
D.
$\frac{2g}{7}$
Q670 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Block A is placed over the block B as shown in figure. Wedge is smooth and fixed. Force of friction on block A is
A.
towards right
B.
towards left
C.
zero
D.
always kinetic
Q671 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A parabolic bowl with its bottom at origin has the shape $y = \frac{x^{2}}{20}$ . Here x and y are in metre. The maximum height at which a small mass m can be placed on the bowl without slipping (coefficient of static friction is 0.5) is
A.
$2.5\mathrm{m}$
B.
$1.25\mathrm{m}$
C.
$1\mathrm{m}$
D.
$4\mathrm{m}$
Q672 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5 \, ms^{-1}$ . The height of the plane of circle from vertex of the funnel is
A.
0.25 cm
B.
2 cm
C.
4 cm
D.
2.5 cm
Q673 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The minimum velocity (in ms $^{-1}$ ) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is
A.
60
B.
30
C.
15
D.
25
Q674 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A bunch of bananas hangs from the end of a rope that passes over a light, frictionless pulley. A monkey of mass equal to the mass of the bananas hangs from the other end of the rope. The monkey and the bananas are initially balanced and at rest. Now the monkey starts to climb up the rope, moving away from the ground with speed v. What happens to the bananas?
A.
They move downward at speed v
B.
They remain stationary
C.
They move up at speed $\frac{1}{2}v$
D.
They move up at speed v
Q675 Advance SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the given arrangement, strings and pulleys are light and all surface are frictionless. Assuming at t = 0, system is released from rest, the speed of block A at t = 2 sec is
A.
$8\mathrm{ms}^{-1}$
B.
$9\mathrm{ms}^{-1}$
C.
$10\mathrm{ms}^{-1}$
D.
None of these