Work, Energy and Power

Particle A of mass m₁ moving with velocity (√3î + ĵ)ms⁻¹ collides with another particle B of mass m₂ which is at rest initially. Let V₁ and V₂ be the velocities of particles A and B after collision respectively. If m₁ = 2m₂ and after collision V₁ = (î + √3ĵ)ms⁻¹, the angle between V₁ and V₂ is:

Blocks of masses m, 2m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8 m starts moving the total energy loss is p% of the original energy. Value of ' p ' is close to:

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height h/2. The velocity versus height of the ball during its motion may be represented graphically by:

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement(s) - time (t) graph that describes the motion of the particle is (graph are drawn schematically and are not to scale):

A block of mass $1.9\mathrm{k}\mathrm{g}$  is at rest at the edge of a table, of height $1\mathrm{m}$ . A bullet of mass  $0.1\mathrm{k}\mathrm{g}$ collides with the block and sticks to it. If the velocity of the bullet is $20\mathrm{m}/\mathrm{s}$  in the horizontal direction just before the combined system strikes the floor, is

[Take $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ . Assume there is no rotational motion and loss of energy after the collision is negligible.]

A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is (g = 10 ms?²)

In a hydrogen atom, an electron makes a transition from (n + 1)th level to the nth level. If n >> 1, the frequency of radiation emitted is proportional to: