Centre of Mass & System of Particles Questions

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 × π ms⁻², what will be the tensile stress developed in the wire?

Distance of the centre of mass of a solid uniform cone from its vertex is z₀. If the radius of its base is R and its height is h then z₀ is equal to (xh/4). What is the value of x?

A highly elastic ball moving at a speed of 3 m/s approaches a wall moving towards it with a speed of 3 m/s. After the collision, the speed of the ball (in m/s) will be:

Two particles are shown in figure. At t = 0, a constant force F = 6N starts acting on the 3 kg mass. Find the velocity of the centre of mass of these particles at t = 5 s, (in m/s).

A particle of mass 2m is projected at an angle of 45° with horizontal with a velocity of 20√2 m/s. After 1 s explosion takes place and the particle is broken into two equal pieces. As a result of explosion one part comes to rest. Find the maximum hei

Two bodies of mass 3 kg and 5 kg have their centre of mass at origin. If 3 kg is at a distance of 5 m from the origin then 5 kg mass is at a distance of:

Two particles of equal mass have velocities v₁ = 2î ms⁻¹ and v₂ = 2ĵ ms⁻¹. First particle has an acceleration a₁ = (3î + 3ĵ) ms⁻² while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a:

A body of mass 20 gm is moving with a certain velocity. It collides with another body of mass 80 gm at rest. The collision is perfectly inelastic. The ratio of the kinetic energies before and after collision of the system is:

Consider following statements: (1) C.O.M of a uniform semicircular disc of radius (R = 2R/π) from the centre (2) C.O.M of a uniform semicircular ring of radius (R = 4R/3π) from the centre(3) C.O.M of a solid hemisphere of radius (R = 4R/3π) from the

Two rods each of mass m and length L are placed along X and Y axis as shown in figure. Coordinates of the centre of mass of the combination is:

A uniform thin rod AB of length L has linear mass density μ(x) = a + bx/L, where x is measured from A. If the CM of the rod lies at a distance of 7L/12 from A, then a and b are related as:

In a ballistics demonstration, a police officer fires a bullet of mass 50 gm with speed 200 m/s. The bullet emerges with only 10% of its initial kinetic energy. The emergent speed of the bullet is:

A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 m/s. The kinetic energy of the other mass is: