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x - axis

y - axis

λ

xL

Special Test

1. The linear mass density of a rod of length L varies, with distance (x) from the left end (x = 0), as shown by the following graph. The centre of mass lies at

A) L B) 2L/3 C) L/3 D) L/2

2. A sphere strikes a wall and rebounds with a velocity of 0.1 m/s at an angle of 60° to the normal to the wall. If the coefficient of restitution is 1/3, the loss of kinetic energy due to collision is

(A) 50% (B) 33% (C) 40% (D) 66%

3. A shot of mass m is fired from a gun of mass M with a velocity u relative to the gun. The actual velocity of the shot is

A)

MuM+m

B)

muM+m

C)

MuM−m

D)

muM−m

4. A rigid body can be hinged about any point on the x-axis. When it is hinged such that the hinge is at x, the moment of inertia is given by I = 2x2 – 12x + 27. The x-coordinate of centre of mass is

(A) x = 2 (B) x = 0 (C) x = 1 (D) x = 3

5. Two boys of equal mass jump off from the rear end of a trolley resting over a smooth horizontal surface with same speed relative to trolley. Select the correct alternative.

A) Trolley attains greater velocity if they jump simultaneously

B) Trolley attains greater velocity if they jump one after the other.

C) Trolley attains same velocity irrespective of the order in which they jump.

D) Trolley does acquire a velocity at all.

6. A uniform sphere of radius 2cm is kept over a rough horizontal surface with coefficient of friction 0.5. A constant horizontal force mg is applied to start its motion from rest. The point of application is at a height h above the horizontal surface. The value of h, for which the sphere slides without rolling, is

A) 1cm B) 0.8 cm C) 2.8cm D) 3 cm

Topics covered

Physics: Kinemtics, Laws of Motion, Work Power Energy

l

v

7. Two particles of equal mass have velocities 4i ms–1 and 4j ms–1. First particle has an acceleration i + j ms–2 while the acceleration of the second particle is zero. The centre of mass of the two particles moves in

(A) a circle (B) a parabola (C) an ellipse (D) a straight line

8. The Force F(N) acting on a body of mass 1 kg is related to its position x(m) as F = x3 – 3x. It is at rest at x = 1, its speed at x = 3 is

(A) 4 m/s (B) 3 m/s (C) 2 m/s (D) 5 m/s

9. A spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring some elongation and released. Select the incorrect option

(A) The block may stop before the spring attains its mean position.

(B) The block must stop with spring having some compression.

(C) The block may stop with spring having some compression.

(D) It is not possible that the block stops at mean position.

10. Two particles each having a mass m are connected by a light rigid rod of length l. The system moves with a velocity and linear velocity of centre of mass is v, vertically downward. When the bar is horizontal, it makes a perfectly elastic impact as shown. Select the correct alternative(s).

A) The linear velocity of centre of mass just after impact is v/2, downwards.

B) The angular velocity of system after impact is 2v/l, clockwise.

C) The rotational and translation kinetic energy of the system get interchanged due to impact.

D) The angular momentum of the system about the centre of mass remains conserved at all moments

Consider the situation shown in figure.The triangular block of mass m is lying at rest on a smooth ground, while the cubical block of same mass m is moving along the incline with a speed v. Assume that during the motion, cubical block does not leave contact with the incline. The acceleration due to gravity is g.

Smooth

Smooth

30°

v

Q.11 The path of the cubicle block in a frame of reference attached with the ground is

a)

b)

c)

d)

Q.12 The work done by the normal contact force between the triangular block and the cubical block on the cubical block as it comes to rest relative to the triangular block is

A)

−18mv2

B)

332mv2

C)

− 332mv2

D) Zero

Q13. The kinetic energy associated with the motion of centre of mass of the two blocks will be equal to sum of the kinetic energies of the two blocks at

A) All instants

B) Initial instants

C) The instant when there is no relative motion between the two blocks

D) No instant

Q.14 Figure shows a very long plank of mass M. Another block of mass m is placed over it. The ground is smooth and there is friction between the block and the plank. The block is imparted an impulse to give it a speed v. Assuming that, the block does not fall down from the plank, the work done by friction force on the system is

Plank ( )Mm v

Sm ooth ground

A)

mMv2

2(M+m)

B)

− mMv2

2(M+m)

C)

m2v2

2(M+m)

D) zero

Q.15 The P.E. of a particle constrained to move along x-axis is given as U = 10 + (x – 3)2 here U is in Joules & x is in meters. Total mechanical energy of particle is 46 J. The movement of the particle is confined to the region bounded by

A) – 3 x 9

B) 3 x 6

C) x 9

D) 3 x 6

Q.16 A physicist hanged a cylinder-shaped container of base 100 cm2 to a spring. He slowly poured water into the container and found that the surface of water remained at the same level. The density of water is 1000 kg/m3.The spring constant of the spring is

A) 1 N/m

B) 100 N/m

C) 1000 N/m

D) 0.001 N/m

Q.17 A 10kg monkey is climbing a massless rope attached to a 15kg mass over a tree limb. The mass is lying on the ground. In order to raise the mass from the ground he must climb with

A) uniform acceleration at least greater than 5m/sec2

B) uniform acceleration at least greater than 2.5m/sec2

C) high speed

D) uniform acceleration at least greater than 10m/sec2

Q.18 In the figure shown a long cart moves on a smooth horizontal surface due to an external constant force of magnitude F. Initial mass of the cart is M0 and velocity is zero. At t = 0 sand starts falling from a stationary hopper on to the cart with negligible velocity at constant rate m kg/s and sticks to the cart. The velocity of the cart at time t (< t0)

A)

t

0

etM

Ft

B)

t

0

eM

Ft

C) 0M

Ft

D) tM

Ft

0

Q.19 System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and g =10 m/s2)

A) 2 m/s B) 22 m/s C) 2 m/s D) 42 m/s

Q.20 Two particles starts moving on the same circle of radius 2 m, from the same point P at t = 0, with constant tangential accelerations = 2 m/s2 and 6 m/s2, clockwise and anticlockwise, respectively. The point where they meet for the first time is Q. The smaller angle subtended by PQ at center of circle is

(A) 120° (B) 60° (C) 135° (D) 90°

Q.21 In an arrangement shown in figure, Let a1, a2 and a3be the ace;eraions of the 1 kg, 2kg and 3kg block then

1 kg

2 kg

3 kg

50 N

= 0.8

= 0.8

= 0.5

(A) a1 = 8 m/s2, a2 = 9 m/s2, a3 = 0

(B) a1 = 8 m/s2, a2 = 9 m/s2, a3 = 9 m/s2

(C) a1 = a2 = 8 m/s2, a3 = 0

(D) a1 = a2 = a3 = 8 m/s2

Q.22 A rod which is very long has a ring slided into it at l = 2 m from one end. Mass of ring is 0.5 kg. Now rod is made to rotate horizontally with the end with a constant angular acceleration a = 1 rad/s2. If the coefficient of friction is 0.5, after what time will ring slide outwards? Neglect gravity.

(A) 1 s (B) 2 s (C) 3 s (D) 4 s

Q.23 Floor and surface of block 2 kg is smooth. Then minimum value of coefficient of friction between 1 kg and 2 kg block such that 1 kg block is stationary with respect to 2 kg block in a figure

2 kg

1 kg

1kg

(A) 2

1

(B) 2

1

(C) 4

1

(D) 3

1

Q.24 A vehicle of mass m starts moving along horizontal circle of radius r, such that its speed varies with distance s covered by vehicles as V = ks where k is constant. Then ratio of centripetal force to that tangential force is

(A) s

r

(B) s

r 2

(C) r

s2

(D) r

s

Q.25 Coefficient of friction between 4 kg block and incline is 0.4 and 2 kg block and incline is 0.2, then find acceleration of both blocks

30°

(A) a = 2.44 m/s2 for 4 kg & a = 2.2 m/s2 for 2 kg

(B) a = 2.44 m/s2 for 4 kg & a = 3.27 m/s2 for 2 kg

(C) Both move with common acceleration of a = 2.11 m/s2

(D) Both move with common acceleration of a = 3 m/s2

Answers

1. C2. D3. A4. D5. B6. A7. D8. A9. D10. B11. B12. C13. C14. B15. A16. B17. A18. D19. B20. D21. (A)22. (A)23. (C)24. (D)25. (C)

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