9
A ball of mass 0.15 kg is dropped from a height 10m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s2) nearly :
10
Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.
The centre of mass of the system from the 5 kg particle is nearly at a distance of :
11
Body A of mass 4m moving with speed u collides with another body B of mass 2 m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :
12
A moving block having mass m, collides with
another stationary block having mass 4m. The
lighter block comes to rest after collision. When
the initial velocity of the lighter block is v, then
the value of coefficient of restitution (e) will be
13
Which of the following statements are correct ?
(1) Centre of mass of a body always coincides with the centre of gravity of the body.
(2) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
(3) A couple on a body produces both translational and rotational motion in a body
(4) Mechanical advantage greater than one means that small effort can be used to lift a large load.
14
Two identical balls A and B having velocities of 0.5 m s$$-$$1 and $$-$$0.3 m s$$-$$1 respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be :
15
A bullet of mass 10 g moving horizontally with a velocity of 400 m s$$-$$1 strikes a wood block of mass 2 kg which is suspended by light inextensible string of length 5 m. As a result, the centre of gravity of the block found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be
17
Two particles of masses m1, m2 move with initial velocities u1 and u2. On collision, one of the particles get excited to higher level, after absorbing energy $$\varepsilon $$. If final velocities of particles be v1 and v2 then we must have :
AIPMT 2015 Cancelled Paper
18
Two spherical bodies of mass M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is :
AIPMT 2015 Cancelled Paper
19
A body of mass (4m) is lying in x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is :
21
A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 m s$$-$$1. The final velocity acquired by the person and the average force exerted on the person are :
22
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m s$$-$$1 and the second part of mass 2 kg moves with 8 m s$$-$$1 speed. If the third part files off with 4 m s$$-$$1 speed, then its mass is :
23
Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin is :
24
Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weights 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by :
25
Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity $${v \over 2}$$ in a direction perpendicular to the original direction. The mass A moves after collision in the direction :
26
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be :
27
Two bodies of mass 1 kg and 3 kg have position vectors $$\widehat i + 2\widehat j + \widehat k$$ and $$ - 3\widehat i - 2\widehat j + \widehat k$$, respectively. The center of mass of this system has a position vector :
28
An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 m s$$-$$1 and 2 kg second part moving with a velocity 8 m s$$-$$1. If the third part flies off with a velocity of 4 m s$$-$$1, its mass would be :
29
A particle of mass m is projected with velocity v making an angle of 45o with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :
30
A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is :
31
A 0.5 kg ball moving with a speed of 12 m/s strikes a hand wall at an angle of 30o with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is :
32
A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 m s$$-$$1. The kinetic energy of the other mass is :
33
Consider a system of two particles having masses m1 and m2. If the particle of mass m1 is pushed towards the mass centre of particles through a distance d. by what distance would be particle of mass m2 move so as to keep the mass centre of particles at the original position?
34
A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1/E2 is :
35
A rod of length is 3 m and its mass acting per unit length is directly proportional to distance x from one of its end then its centre of gravity from that end will be at :
36
If kinetic energy of a body is increased by 300% then percentage change in momentum will be :
37
A disc is rolling, the velocity of its centre of mass is vcm. Which one will be correct?
