2. A sledge moving over a smooth horizontal surface of ice at a velocity v0 drives out on a horizontal road and comes to a halt as shown. The
sledge has a length l, mass m and friction between runners and road is µ
A) No work is done by the friction to switch the sledge from ice to the road
B) A work of 2
1µmgl is done against friction while sledge switches completely on to
road
C) The distance covered by the sledge on the road is
µ
g
−2 2
v
20 lD) Total distance moved by the sledge before stopping is
moving with a constant speed
A) The speed of the insect as seen from the ground is <
t
D) The total kinetic energy of the system is 2
4. Two blocks A and B each of mass m are connected by a light spring of natural length L and spring constant k.
The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown. A
third identical block C, also of mass m, moves on the floor with a speed v along the line joining A to B and collides with A. Then
A) the kinetic energy of the A-B system at maximum compression of the spring is zero B) the kinetic energy of the A-B system at maximum compression of the spring is
C) the maximum compression of the spring is
D) the maximum compression of the spring is
section of the car and ρ is the density of air then
A) Power loss due to air resistance is 2
6. A heavy mass M resting on the ground is connected to a lighter mass m through a light inextensible string passing over a light, frictionless pulley as shown in the figure. The string connected to mass M is loose. Let lighter mass m be allowed to fall freely through a height h such that the string becomes taut. If t is the time from this instant onwards when the heavier mass again makes contact with the ground and
∆E is the change in kinetic then A) t = the force F acting on the body is such that
A) F ∝ t1/2 B) F ∝ t-1/2 C) F ∝ v D) F ∝ v-1
8. A car of mass m is moving on a level road at a constant speed vmax while facing a resistive force R. If the car slows down to vmax/3, then assuming the engine to be working at the same power, what force F is developing and what is the acceleration a of the car ?
A) F = 3R B) F = 2R
C) a = 3P/m vmax D) a = 2 P/m vmax
9. The net interacting force F between two particles is related to the distance x between them, as shown in figure. Then
A) potential energy of the system decreases from x1 to x2
B) potential energy of the system increases from x2 to x3
C) potential energy of the system decreases from x3 to x4
D) kinetic energy increases from x1 to x2
10. The potential energy of a particle of mass 1 kg moving in xy plane is given by U = 10 - 4x - 3y
The particle is at rest at (2, 1) at t = 0. Then
A) velocity of particle at t = 1 is 5 m/s B) the particle is at (10m, 7m) at t = 2s C) work done during t = 1s to t = 2s is 75J
D) the magnitude of force acting on particle is 5N
11. The figure shows a potential energy function. In the region 0 ≤ r ≤ R, U(r) is parabolic. In the region r ≥ R, U(r) is an inversely proportional function.
Identify the correct conservative force function F(r) plot.
(A) (B) (C) (D)
12. The potential energy function between two atoms in a diatomic molecule can be plotted as shown in figure.
Mark the correct statement(s):
A) There is only one position of equilibrium B) There is two position of equilibrium
C) There is only one position of stable equilibrium D) Both the positions are of stable equilibrium
13. A block of mass m is gently placed on a vertical spring of stiffness k. Choose the correct statement related to the mechanical energy E of the system.
A) It remains constant B) It decreases C) It increases D) Nothing can be said
14. A spring of stiffness k is pulled by two forces FA and FB as shown in the figure so that the spring remains in equilibrium. Identify the correct statement(s):
A) The work done by each force contributes into the increase in potential energy of the spring
B) The force undergoing larger displacement does positive work and the force undergoing smaller displacement does negative work
C) Both the forces perform positive work
D) The net work done is equal to the increase in potential energy
15. A particle of mass m is released from a height H on a smooth curved surface which ends into a vertical loop of radius R, as shown in figure.
If θ is the instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical, the identify the correct statement(s) related to the normal reaction N between the block and the surface.
A) The maximum value N occurs at θ = 0 B) The minimum value of N occurs at N
= π
C) The value of N becomes negative for π/2 < θ <
2 3π D) The value of N becomes zero only when θ > π/2
16. An engine is pulling a train of mass m on a level track at a uniform speed v. The resistive force offered per unit mass is f
A) Power produced by the engine is mfv
B) The extra power developed by the engine to maintain a speed v up a gradient of h in s is s
mghv
C) The frictional force exerting on the train is mf on the level track D) None of above is correct
17. A particle of mass 5 kg moving in the x-y plane has its potential energy given by U = (-7x + 24y) J, where x and y are in metre. The particle is initially at origin and has a velocity ur=(14.4iˆ+4.2jˆ)ms−1
A) The particle has a speed of 25 ms-1 at t = 4 s B) The particle has an acceleration of 5 ms-2
C) The acceleration of the particle is perpendicular to its initial velocity D) None of the above is correct
18. A particle is moving in a conservative force field from point A to point B. UA and UB are the potential energies of the particle at points A and B and Wc is the work done in the process of taking the particle from A to B
A) Wc = UB - UA B) Wc = UA - UB C) UA > UB D) UB > UA
19. At the position of stable equilibrium
A) =
dx
dU 0 only B) dx
du= 0 and
2 2
dx U
d > 0 C) 0 dx
dU= and 0
dx U d
2
2 < D) None of
these
20. Choose the correct statement(s) related to the conservative force and potential energy.
A) Potential energy decrease in the direction of conservative force B) Potential energy increase in the direction of conservative force C) Conservative force does work by lowering its potential energy D) Conservative force does work by raising its potential energy KEY
1 2 3 4 5 6 7 8 9 10
AC BCD AC BD AC BC BD AD ABD ABD
11 12 13 14 15 16 17 18 19 20
A BC B ACD ABD ABC ABC BC C BC