Center of Mass and Collision

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point $A\left(\theta=\frac{\pi}{2}\right)$ with identical uniform angular speeds in opposite dir...

Bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length 10 m , as shown in the figure. Point mass $A$ of mass $m$ travelling horizontally with speed $10 \mathrm{~ms}^{-1}$ hits bob $B$ elastically....

A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and rises to a height of 10 m . The impulse imparted to the ball during its collision with the ground is (Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

Two bodies \(A\) and \(B\) of same mass undergo completely inelastic one dimensional collision. The body \(A\) moves with velocity \(v_1\) while body \(B\) is at rest before collision. The velocity of the system after collision is \(v_2\). ...

A \(1 \mathrm{~kg}\) object strikes a wall with velocity \(1 \mathrm{~m} \mathrm{~s}^{-1}\) at an angle of \(60^{\circ}\) with the wall and reflects at the same angle. If it remains in contact with wall for \(0.1 \mathrm{~s}\), then the for...

Two particles A and B initially at rest, move towards each other under mutual force of attraction. At an instance when the speed of A is v and speed of B is 3v, the speed of centre of mass is :

A bullet of mass \(m\) hits a block of mass \(M\) elastically. The transfer of energy is the maximum, when :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : When a fire cracker (rocket) explodes in mid air, its fragments fly in such a way that they continue moving in the sa...

The distance covered by a body of mass 5 g having linear momentum 0.3 kg m/s in 5 s is :

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is :

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) f...

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 :

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 :

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 :

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...

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...

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 vert...

A rigid ball of mass m strikes a rigid wall at 60o and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be :

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 :

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...

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 sma...

The force F acting on a particle of mass m is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is :

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 :

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 b...

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 spe...

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 ...

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 ...

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 :

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 :

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 fli...

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 :

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 :

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 :

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 t...

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 :

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 ...

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 :

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 :

If kinetic energy of a body is increased by 300% then percentage change in momentum will be :

A disc is rolling, the velocity of its centre of mass is vcm. Which one will be correct?