Center of Mass and Collision

A uniform rectangular thin sheet ABCD of
mass M has length a and breadth b, as shown
in the figure. If the shaded portion HBGO is
cut-off, the coordinates of the centre of mass
of the remaining portion will be :-

A simple pendulum, made of a string of length \(\ell\) and a bob of mass m, is released from a small angle \({{\theta _0}}\). It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It
b...

The position vector of the centre of mass \(\overrightarrow r {\,_{cm}}\,\) of an asymmetric uniform bar of negligible area of crosssection as shown in figure is :

An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The
man pushes his son so that he starts moving at a speed of 0.70 ms–1 with respect to the man. The speed of the
man with respect to ...

Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side
1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :

A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 \(\times\) 106 N/m. The body sticks to the platform and the spring's maximum compression is fou...

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a consta...

A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then...

Two particles, of masses M and 2M, moving,
as shown, with speeds of 10 m/s and 5 m/s,
collide elastically at the origin. After the
collision, they move along the indicated
directions with speeds u1 and u2, respectively.
The values of u1 and...

A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90o with respect to each other. The mass of unknown particle is :

The mass of a hydrogen molecule is 3.32 \(\times\) 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on t...

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If
the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative
velocity between ...

Two particles A and B of equal mass M are moving with the same speed \(\upsilon\) as shown in the figure. They collide completely inelastically and move as a single particle C. The angle \(\theta\) that the path of C makes with the X-axis...

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then \({{BC} \over {AB}}\) is close to :

A neutron moving with a speed ‘v’ makes a head on collision with a stationary
hydrogen atom in ground state. The minimum kinetic energy of the neutron for
which inelastic collision will take place is :

A particle of mass \(m\) moving in the \(x\) direction with speed \(2v\) is hit by another particle of mass \(2m\) moving in the \(y\) direction with speed \(v.\) If the collision is perfectly inelastic, the percentage loss in the energy ...

Distance of the center of mass of a solid uniform cone from its vertex is \(z{}_0\). If the radius of its base is \(R\) and its height is \(h\) then \(z{}_0\) is equal to :

This question has statement \({\rm I}\) and statement \({\rm I}\)\({\rm I}\). Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - \({\rm I}\): A point particle of mass \(m\) mov...

Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement - 2 : Principle of conservation of momentum holds true for all kinds of collisions.

The figure shows the position\(-\)time \((x-t)\) graph of one-dimensional motion of body of mass \(0.4\) \(kg.\) The magnitude of each impulse is

A block of mass \(0.50\) \(kg\) is moving with a speed of \(2.00\) \(m{s^{ - 1}}\) on a smooth surface. It strike another mass of \(1.0\) \(kg\) and then they move together as a single body. The energy loss during the collision is :

A thin rod of length \('L'\) is lying along the \(x\)-axis with its ends at \(x=0\) and \(x=L\). Its linear density (mass/length) varies with \(x\) as \(k{\left( {{x \over L}} \right)^n},\) where \(n\) can be zero or any positive number. If...

A circular disc of radius \(R\) is removed from a bigger circular disc of radius \(2R\) such that the circumferences of the discs coincide. The center of mass of the new disc is \(\alpha R\) form the center of the bigger disc. The value of ...

A player caught a cricket ball of mass \(150\) \(g\) moving at a rate of \(20\) \(m/s.\) If the catching process is completed in \(0.1s,\) the force of the blow exerted by the ball on the hand of the player is equal to

Consider a two particle system with particles having masses \({m_1}\) and \({m_2}\). If the first particle is pushed towards the center of mass through a distance \(d,\) by what distance should the second particle is moved, so as to keep th...

A bomb of mass \(16kg\) at rest explodes into two pieces of masses \(4\) \(kg\) and \(12\) \(kg.\) The velocity of the \(12\) \(kg\) mass is \(4\,\,m{s^{ - 1}}.\) The kinetic energy of the other mass is

A mass \('m'\) moves with a velocity \('v'\) and collides inelastically with another identical mass. After collision the \({1^{st}}\) mass moves with velocity \({v \over {\sqrt 3 }}\) in a direction perpendicular to the initial direction of...

The block of mass \(M\) moving on the frictionless horizontal surface collides with the spring of spring constant \(k\) and compresses it by length \(L.\) The maximum momentum of the block after collision is

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force \('\,\,\overrightarrow F \,\,'\) is applied at the point \(P\) parallel to \(AB,\) such that the object has only the translational motion without rot...

A body \(A\) of mass \(M\) while falling vertically downloads under gravity breaks into two-parts; a body \(B\) of mass \({1 \over 3}\) \(M\) and a body \(C\) of mass \({2 \over 3}\) \(M.\) The center of mass of bodies \(B\) and \(C\) taken...

A machine gun fires a bullet of mass \(40\) \(g\) with a velocity \(1200m{s^{ - 1}}.\) The man holding it can exert a maximum force of \(144\) \(N\) on the gun. How many bullets can he fire per second at the most?

Consider the following two statements :
\(A.\) Linear momentum of a system of particles is zero
\(B.\) Kinetic energy of a system of particles is zero.
then

Two identical particles move towards each other with velocity \(2v\) and \(v\) respectively. The velocity of center of mass is