Question 1: Palette 1/29

JEE Advanced 2020 MSQ

A student skates up a ramp that makes an angle 30$^\circ$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v₀ and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

A

$v_0^2 - 2gh = {1 \over 2}gR$

B

$v_0^2 - 2gh = {{\sqrt 3 } \over 2}gR$

C

the centripetal force required at points x and z is zero

D

the centripetal force required is maximum at points x and z

Question 2: Palette 2/29

JEE Advanced 2019 MSQ

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure.



When the distance of the piston from closed end is L = L₀, the particle speed is v = v₀. The piston is moved inward at a very low speed V such that $V < < {{dL} \over L}{v_0}$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?

A

After each collision with the piston, the particle speed increases by 2V.

B

If the piston moved inward by dL, the particle speed increases $2v{{dL} \over L}$.

C

The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L₀ to 1/2 L₀.

D

The rate at which the particle strikes the piston is v/L.

Question 3: Palette 3/29

JEE Advanced 2018 MSQ

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK/dt = \gamma t,$ where $\gamma $ is a positive constant of appropriate dimensions. Which of a positive constant of appropriate dimensions. Which of the following statement is (are) true?

A

The force applied on the particle is constant

B

The speed of the particle is proportional to time

C

The distance of the particle from the origin increases linearly with time

D

The force is conservative

Question 4: Palette 4/29

JEE Advanced 2018 MCQ

In the List-${\rm I}$ below, four different paths of a particle are given as functions of time. In these functions, $\alpha $ and $\beta $ are positive constants of appropriate dimensions and $\alpha \ne \beta $ In each case, the force acting on the particle is either zero or conservative. In List-${\rm I}{\rm I}$, five physical quantities of the particle are mentioned $\overrightarrow p $ is the linear momentum, $\overrightarrow L $ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy. Match each path in List-${\rm I}$ with those quantities in List-${\rm II}$, which are conserved for that path.

LIST - I		LIST - II
P.	$\overrightarrow r $(t)=$\alpha $ $t\,\widehat i + \beta t\widehat j$	1.	$\overrightarrow p $
Q.	$\overrightarrow r \left( t \right) = \alpha \cos \,\omega t\,\widehat i + \beta \sin \omega t\,\widehat j$	2.	$\overrightarrow L $
R.	$\overrightarrow r \left( t \right) = \alpha \left( {\cos \omega t\,\widehat i + \sin \omega t\widehat j} \right)$	3.	K
S.	$\overrightarrow r \left( t \right) = \alpha t\,\widehat i + {\beta \over 2}{t^2}\widehat j$	4.	U
		5.	E

A

$P \to 1,2,3,4,5;\,Q \to 2,5;R \to 2,3,4,5;S \to 5$

B

$P \to 1,2,3,4,5;{\mkern 1mu} Q \to 3,5;R \to 2,3,4,5;S \to 2,5$

C

$P \to 2,3,4;{\mkern 1mu} Q \to 5;R \to 1,2,4;S \to 2,5$

D

$P \to 1,2,3,4,5;{\mkern 1mu} Q \to 2,5;R \to 2,3,4,5;S \to 2,5$

Question 5: Palette 5/29

JEE Advanced 2017 MSQ

A flat plate is moving normal to its plane through a gas under the reaction of a constant force $F.$ The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed u of the gas molecules.

Which of the following options is /are true?

A

The pressure difference between the leading and trailing faces of the plate is proportional to uv

B

The resistive force experimenced by the plate is proportional to $v$

C

The plate will continue to move with constant non-zero acceleration, at all times

D

At a later time the external force $F$ balances the resistive force

Question 6: Palette 6/29

JEE Advanced 2015 MCQ

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in Column I (a and U₀ are constants). Match the potential energies in Column I to the corresponding statement(s) in Column II:

A

(A)→(P), (Q), (R); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)

B

(A)→(P), (Q), (R), (T); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)

C

(A)→(P), (Q), (R), (T); (B)→(Q); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)

D

(A)→(P), (Q), (R), (T); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R)

Question 7: Palette 7/29

JEE Advanced 2014 MCQ

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale.

A

B

C

D

Question 8: Palette 8/29

JEE Advanced 2013 MCQ

The magnitude of the normal reaction that acts on the block at the point Q is

A

7.5 N

B

8.6 N

C

11.5 N

D

22.5 N

Question 9: Palette 9/29

JEE Advanced 2013 MCQ

The speed of the block when it reaches the point Q is

A

5 ms^-1

B

10 ms^-1

C

$10\sqrt 3 $ ms^-1

D

20 ms^-1

Question 10: Palette 10/29

JEE Advanced 2013 MCQ

The work done on a particle of mass m by a force $$K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat i + {y \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat j} \right]$$ (K being a constant of appropriate dimensions), when the particle is taken from the point $\left( {a,0} \right)$ to the point $\left( {0,a} \right)$ along a circular path of radius a about the origin in the x-y plane is

A

${{2K\pi } \over a}$

B

${{K\pi } \over a}$

C

${{K\pi } \over {2a}}$

D

0

Question 11: Palette 11/29

JEE Advanced 2011 MSQ

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision,

A

the ring has pure rotation about its stationary CM.

B

the ring comes to a complete stop.

C

friction between the ring and the ground is to the left.

D

there is no friction between the ring and the ground.

Question 12: Palette 12/29

JEE Advanced 2010 MCQ

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 s is

A

4.50 J

B

7.50 J

C

5.06 J

D

14.06 J

Question 13: Palette 13/29

JEE Advanced 2008 MCQ

A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio $\frac{y}{x}$ is :

A

4

B

2

C

$\frac{1}{2}$

D

$\frac{1}{4}$

Question 14: Palette 14/29

JEE Advanced 2008 MCQ

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle $\theta$ at which the speed of the bob is half of that at A, satisfies,

A

$\theta = {\pi \over 4}$

B

${\pi \over 4} < \theta < {\pi \over 2}$

C

${\pi \over 2} < \theta < {{3\pi } \over 4}$

D

${{3\pi } \over 4} < \theta < \pi $

Question 15: Palette 15/29

JEE Advanced 2007 MCQ

Statement 1 :

A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30$^\circ$ with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

Statement 2 :

The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

A

Statement 1 is True, Statement 2 is True, Statement 2 is a CORRECT explanation for Statement 1

B

Statement 1 is True, Statement 2 is True, Statement 2 is NOT a CORRECT explanation for Statement 1

C

Statement 1 is True, Statement 2 is False

D

Statement 1 is False, Statement 2 is True

Question 16: Palette 16/29

JEE Advanced 2006 MSQ

A ball moves over a fixed track as shown in the figure. From $A$ to $B$, the ball rolls without slipping. Surface $B C$ is frictionless. $K_A, K_B$ and $K_c$ are kinetic energies of the ball at $A, B$ and C , respectively. Then

A

$h_{\mathrm{A}}>h_{\mathrm{c}^{\prime}} \mathrm{K}_{\mathrm{B}}>\mathrm{K}_{\mathrm{C}}$.

B

$h_{\mathrm{A}}>h_{\mathrm{c}} ; \mathrm{K}_{\mathrm{C}}>\mathrm{K}_{\mathrm{A}}$.

C

$h_{\mathrm{A}}=h_{\mathrm{c}} ; \mathrm{K}_{\mathrm{B}}=\mathrm{K}_{\mathrm{C}}$.

D

$h_{\mathrm{A}} < h_{\mathrm{c}} ; \mathrm{K}_{\mathrm{B}}>\mathrm{K}_{\mathrm{C}}$.

Question 17: Palette 17/29

JEE Advanced 2004 MCQ

A particle is acted by a force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x

A

B

C

D

Question 18: Palette 18/29

JEE Advanced 2003 MCQ

If W₁, W₂ and W₃ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W₁, W₂ and W₃.

A

W1 > W2 > W3

B

W1 = W2 = W3

C

W1 < W2 < W3

D

W2 > W1 > W3

Question 19: Palette 19/29

JEE Advanced 2002 MCQ

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

A

${{4Mg} \over k}$

B

${{2Mg} \over k}$

C

${{Mg} \over k}$

D

${{Mg} \over {2k}}$

Question 20: Palette 20/29

JEE Advanced 2000 MCQ

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

A

v

B

v²

C

v³

D

v⁴

Question 21: Palette 21/29

JEE Advanced 1999 MCQ

A spring of force-constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of

A

$\left( {{2 \over 3}} \right)k$

B

$\left( {{3 \over 2}} \right)k$

C

3 k

D

6 k

Question 22: Palette 22/29

JEE Advanced 1998 MCQ

A force $F = - K\left( {y\widehat i + x\widehat j} \right)$ (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point $\left( {a,0} \right)$, and then parallel to the y axis to the point $\left( {a,a} \right)$. The total work done by the force F on the particle is

A

$ - 2K{a^2}$

B

$2K{a^2}$

C

$ - K{a^2}$

D

$K{a^2}$

Question 23: Palette 23/29

JEE Advanced 1998 MCQ

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A

$\sqrt {{u^2} - 2gL} $

B

$\sqrt {2gL} $

C

$\sqrt {{u^2} - gL} $

D

$\sqrt {2\left( {{u^2} - gL} \right)} $

Question 24: Palette 24/29

JEE Advanced 1994 MCQ

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ${a_c}$ is varying with time t as ${a_c}$ = k²rt² where k is a constant. The power delivered to the perticles by the force acting on it is:

A

$2\pi m{k^2}{r^2}t$

B

$m{k^2}{r^2}t$

C

${{\left( {m{k^4}{r^2}{t^5}} \right)} \over 3}$

D

zero

Question 25: Palette 25/29

JEE Advanced 1987 MSQ

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that :

A

Its velocity is constant

B

its acceleration is constant

C

its kinetic energy is constant

D

it moves in a circular path

Question 26: Palette 26/29

JEE Advanced 1985 MCQ

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is

A

MgL

B

${{MgL} \over 3}$

C

${{MgL} \over 9}$

D

${{MgL} \over {18}}$

Question 27: Palette 27/29

JEE Advanced 1984 MCQ

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in the time t is proportional to

A

t^1/2

B

t^3/4

C

t^3/2

D

t²

Question 28: Palette 28/29

JEE Advanced 1980 MCQ

If a machine is lubricated with oil

A

the mechanical advantage of the machine increases

B

the mechanical efficiency of the machine increases

C

both its mechanical advantage and efficiency increases

D

its efficiency increases, but its mechanical advantage decreases

Question 29: Palette 29/29

JEE Advanced 1980 MCQ

Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is

A

4 : 1

B

$\sqrt 2 :1$

C

$1:2$

D

1 : 16