Question

A lift is moving with acceleration 2 m/s-2 in upward direction. A bolt from ceiling of lift starts to fall. If height of lift is 6 m. Then time taken by bolt to hit
the floor of lift is​

Answer 1

lift is moving upward with acceleration 2m/s². so, lift is an non-inertial frame of reference. but we know, we can't apply Newtonian equation in case of non-inertial frame. to make it inertial frame, apply pseudo force just opposite it and equal in magnitude.

so, pseudo force , P = m(2)

and weight of bolt, F = m(g)

then, net force = ma = mg + m2 =>a = (g + 2)

so, net acceleration acting on bolt, a = (g + 2) = 12m/s²

given, height of lift , h = 6m

initial velocity of bolt , u = 0

then, h = ut + 1/2 at²

or, 6 = 0 + 1/2 × (12) × t²

or, 6 = 6t² => t = 1

hence, time taken by bolt to hiy the floor of the lift is 1sec.