Q.1 A small block of mass 2m initially rests at the bottom of a fixed circular, vertical track, which has a radius of R. The contact surface between the mass and the loop is frictionless. A bullet of mass m strikes block horizontally with initial speed v0 and
2i ˆ 2 j ˆ
ˆ ˆ i j
vp
A B
remain embedded in the block as the block and the bullet circle the loop. Choose the correct options –
(A) The speed of masses immediately after the impact is v0/3
(B) The min. initial speed of the bullet if the block and the bullet are to successfully execute a complete ride on the loop is
(C) The min. initial speed of the bullet if the block and the bullet are to successfully execute a complete ride on the loop is
(D) The speed of the masses immediately after the impact is v0/2 Q.2 X and Y components of acceleration of C. M. are
(A) (B)
(C) (D)
Q.3 A projectile is projected at a speed u at an angle
into two fragments of mass ratio 1 : 2. The smaller fragments coming to rest. Then : (A) In a given time both parts will cover equal vertical displacement
(B) The distance of heavier fragments from the point of projection is 4R/3 where R is horizontal range.
(C) The distance of heavier fragments from the point of projection is 5R/4 (D) Linear momentum is conserved only in Y direction.
Q.4 P is the centre of mass of four point masses A, B, C & D which are coplanar but not collinear.
(a) P may or may not coincide with one of the point masses.
(b) P must lie within the quadrilateral ABCD
(c) P must lie within or on the edge of at least one of the triangles formed by taking A, B, C and D three at a time.
(d) P must lie on a line joining two of the point A, B, C, D.
Q.5 A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined system (bag + bullet) :
(A) Momentum is mv/(M + m) (B) KE is (1/2) Mv2 (C) Momentum is mv (D) KE is m2v2/2(M + m}
Q.6 A solid cone and a solid sphere is arranged as shown in the figure.
2m R
m,v0
3 5gR
3 3gR
1 2 CM X
1 2
m m g (a )
m m
1 2
CM X 2
1 2
m m g (a )
(m m )
2 2 CM Y
1 2
(a ) m g
m m
2 CM Y
1 2
(a ) m g
m m
The centre of mass is :
(A) at 3R if m1 = m2 = m and R1 = R2
(B) at 1 2 and R1 = R2
1 2 then distance from the centre of solid cone is 11R/3 (D) at 1.5R if m1 = m2 = m and R1 = R2
Q.7 In head on elastic collision of two bodies of equal masses
(A) the velocities are interchanged (B) the speeds are interchanged
(C) the momenta are interchanged (D) the faster body slows down and the slower body speeds up.
Q.8 An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown.
Which of following cannot be centre of mass of the object.
(A) (R/3, R/3) (B) (R/3, R/2)
(C) (R/4, R/4) (D)
Q.9 Mass m1 hits and sticks with m2 while sliding horizontally with velocity v along the common line of centres of the three equal masses (m1 = m2 = m3 = m). Initially masses m2 and m3 are stationary and the spring is unstretched. Choose the correct options
(A) the velocities of m1, m2 and m3 immediately after impact are v/2, v/2, 0 (B) the maximum kinetic energy of m3 is 2mv2/9
(C) the minimum kinetic energy of m2 is mv2/72
(D) max. compression of spring is
Q.10 A man of mass M is carrying a ball of the mass M/2. The man is initially in the state of rest at a distance D from fixed vertical wall. He throws the ball towards the wall with a velocity V with respect to earth at t = 0.
y
A x B
////////////////////////////////////////////////////////////////////////////////////////////////////////
m1 v m2 k m3
Frictionless
m v
6k
As a result of throwing, the man also starts moving backwards. The ball rebounds elastically from the wall.
The man finally collects the ball. Assuming friction to be absent.
(A) the velocity of the man + ball system after the man has collected the ball is 2V/3 (B) impulse by ball on man is MV/3
(C) impulse by ball on man is MV/6 (D) he catches the ball again at t = 4D/V
Q.11 Two cars initially at rest are free to move in the x direction. Car A has mass 4 kg and car B has mass 2 kg.
They are tied together, compressing a spring in between them. When the spring holding them together is burned, car A moves off with a speed of
2m/s. Choose the correct options –
(A) The speed with which car B leave is 4 m/s (B) Energy stored in the spring before it was burned is 24 J
(C) The speed with which car B leave is 2 m/s (D) Energy stored in the spring before it was burned is 12 J
Q.12 Choose the incorrect statements
(B) CM of a uniform semicircular ring of radiu
(D) CM of a hemisphere shell of radius R = R/2 from the centre Q.13 A smooth ball of mass 1 kg is projected with
velocity 7 m/s horizontally from a tower of height 3.5m. It collide elastically with wedge of mass 3 kg and inclination 45° kept on ground. Ball collides the wedge at a height of 1m above the ground. (Neglect friction at any contact) Choose the correct options –
(A) The velocity of the wedge after collision is 4 m/s.
(B) The velocity of the ball after collision is
(C) The velocity of the wedge after collision is 7 m/s.
(D) The velocity of theball after collision is 14 m/s
1 kg 7m/s
3.5m
45°1m 3kg
5 2 m / s
Q.14 normal to the surface at the point of contact & rebounds at
(A) (B)
Q.15 In an inelastic collision –
(A) the velocity of both the particles may be same after the collision (B) kinetic energy is not conserved
(C) linear momentum of the system is conserved
(D) velocity of separation will be less than velocity of approach.
Q.16 Two particles, P of mass 2m and Q of mass m, are subjected to mutual force of attraction and no other force acts on them. At
t = 0, P is at rest at point O and Q is moving away from O with a speed 5u. At a later instant t = T (before any collision has taken place), Q is moving towards O with speed u. Then –
(A) momentum of particle P at t = T is zero (B) momentum of particle P at t = T is 6mu
2 –3 mu2
Q.17 Three carts move on a frictionless track with inertias and velocities as shown. The carts collide and stick together after successive collisions. Choose the correct options
(A) Loss of mechanical energy when B and C stick together is 3 J
(B) Magnitude of impulse experienced by A when it sticks to combined mass (B and C) is 12/5 Ns (C) Loss of mechanical energy when B and C stick together is 1.5 J
(B) Magnitude of impulse experienced by A when it sticks to combined mass (B and C) is 5/12 Ns
Q.18 The simple pendulum A of mass mA B. If the system
–
(A) The velocity vB
s 3mAg +
////////////////////////////////////////////////////////////////////////////////////////////////////////
m = 2kg v = 1m/s
1 1
m = kg v = 1m/s
2 2
1 m = 2kg
v = m/s
3 3
2
A B C
+ve
q A B
A B A
B
m 2g
m m
1m 2
A B
m g
m
(C) The velocity vB
Ag +
Q.19 In which of the following cases the centre of mass of a rod is certainly not at its centre?
(A) density continuously increments from left to right
(B) density continuously decrements from left to right (C) density decreases from left to right upto the centre and then increments (D) density increases from left to right upto the centre & then decreases
Q.20 A body is moving towards a finite body which is initially at rest collides with it. In the absence of any external impulsive force, it is possible that
(A) both the bodies come to rest (B) both bodies move after collision
(c) the moving body comes to rest & stationary body starts moving
(D) the stationary body remains stationary, moving body changes its velocity.
Q.21
The density at one end being twice that of the other end. Choose the correct options–
(A) An expression for linear mass density as a function of distance x from end A where linear mass density
0 is
(B) The position of the centre of mass from end A is 7/9 L
(C) An expression for linear mass density as a function of distance x from end A where linear mass density
0 is
(D) The position of the centre of mass from end A is 5/9 L
Q.22 In a one-dimensional collision between two particles, their relative velocity is before the collision and after the collision
(A) if the collision is elastic (B) if the collision is inelastic
(C) in all cases (D) in all cases, where k
Q.23 lifted
vertically with constant velocity by a force P.
2) (B) no energy will loss in this process
(C) work done by force will be
(D) Loss in energy
B A A
B
m 2g
m m
1
m
2 A B2m g m
x 2L
x L
1 2
v v v
1 v
22 1
| v | | v | v 1 kv 2
2 2
1 gL v L 2r + r
1
22 r gLv
Q.24 A sphere A is released from rest in the position shown and the strikes the block B which is at rest. If e = 0.75 between A and B and µk = 0.5 between B and the support. Choose the correct options –
(A) the velocity of A just after the impact is
(B) the maximum displacement of B after the impact
(C) the velocity of A just after the impact is
(D) the maximum displacement of B after the impact Q.25 A rod of mass M – m carries an insect of mass m at its
bottom end and its top end is connected with a string which passes over a smooth pulley and the other end of the string is connected to a counter mass M. Initially the insect is at
rest. Choose the correct option(s) –
(A) As insect starts moving up relative to rod, the acceleration of centre of mass of the system (insect + rod + counter mass) becomes non-zero.
(B) As insect starts moving up relative to rod, tension in the string remains constant and is equal to Mg.
(C) An insect starts moving up relative to rod, the tension in the string becomes more than Mg (D) Acceleration of centre of mass of the system (insect + rod + counter mass) is zero when insect moves with constant velocity.
Q.26 If the external forces acting on a system have zero resultant, centre of mass (A) must not move (B) must not accelerate
(C) may move (D) may accelerate
Q.27 In a one dimensional collision between two identical particles A and B, B is stationary and A has momentum p before impact. During its impact B gives impulse J to A.
(A) The total momentum of the ‘A plus B’ system is p before and after the impact, and (p-J) during the impact
(B) During the impact A gives impulse of magnitude J to B
(C) The coefficient of restitution is (D) The coefficient of restitution is B
4kg 1.5m 2kg 90°
A
g / 6 m / s 49 m 48 g / 12 m / s
37 m 48
/////////////
M M–m
m
2J 1
p J
p 1
Q.28 A body is thrown vertically upwards from ground with a speed of 10 m/s. If coefficient of restitution of ground, e = 1/2. Choose the correct options –
(A) The total distance travelled by the time it almost stops is 20/3 m
(B) Time elapsed (after the ball has been thrown) when it is at its subsequent maximum height for the third time is 6.25 sec.
(C) The total distance travelled by the time it almost stops is 40/3 m
(D) Time elapsed (after the ball has been thrown) when it is at its subsequent maximum height for the third time is 3.25 sec.
Q.29 A block moving in air explodes in two parts then just after explosion
(A) the total momentum must be conserved (B) the total kinetic energy must be conserved (C) the total momentum must change (D) the total kinetic energy must increase
Q.30 A smooth sphere A of mass 0.1 kg is moving with speed 5m/s when it collides head on with another smooth stationary sphere of same radius. If A is brought to rest by the impact and e = 1/2. Choose the correct options –
(A) The mass of B is 0.2 kg (B) Speed of B just after impact is 2.5 m/s (C) Magnitude of impulse during collision is 0.5 Ns (D) Speed of B just after impact is 1.5 m/s Q.31 In a game of Carom Board, the Queen (a wooden
disc of radius 2cm. and mass 50gm) is placed at the exact center of the horizontal board. The striker is a smooth plastic disc of radius 3cm. and mass 100gm.
The board is frictionless. The striker is given an initial velocity u parallel to the sides BC or AD so that it hits the Queen inelastically with coefficient of restitution = 2/3. The impact parameter for the collision is ‘d’ (shown in the figure). Queen rebounds from
edge AB of the board inelastically with same coefficient of restitution = 2/3 and enters the hole D following the dotted
path shown. The side of the board is L. Choose the correct options –
(A) The value of impact parameter ‘d’ is
(B) The time which the Queen takes to enter hold D after collision with the striker is
(C) The value of impact parameter ‘d’ is
(D) The time which the Queen takes to enter hold D after collision with the striker is Q.32 In an elastic collision in absence of external force, which of the following is/are correct:
A L B
D C
d u L
5 cm 17
153L 40u
2 cm 17
153L
80u
(A) The linear momentum is conserved
(B) The potential energy is conserved in collision
(C) The final kinetic energy is less than the initial kinetic energy (D) The final kinetic energy is equal to the initial kinetic energy
Q.33 A particle of mass m moving with a velocity m/s collides with stationary body of mass M and finally moves with velocity m/s. Then
(A) Impulse received by (B) Impulse received by
(C) Impulse received by (D) Impulse received by
Q.34 A particle of mass m1 (A) elastically collides with another stationary particle (B) of mass m2. Then :
(A) and the particles fly apart in the opposite direction with equal velocities.
(B) and the particles fly apart in the opposite direction with equal velocities.
(C) and the collision angle between the particles is 60° symmetrically.
(D) and the particles fly apart symmetrically at an angle 90°
Q.35 A block of mass m moving with a velocity v0 collides with a stationary block of mass M at the back of which a spring of stiffness k is attached, as shown in figure. Choose the correct alternative(s).
(A) The velocity of the centre of mass is v0/2
(B) initial kinetic energy of system in the centre of mass frame is
(C) maximum compression in spring is
(D) When the spring is in the state of maximum compression, the kinetic energy in the centre of mass frame is zero