A rectangular solid box of length 0.3 m is held horizontally, with… | JEE Main 2019 (8 Apr, Shift 2)

Q60JEE Main 2019 · 8 APR · SHIFT 2Difficult

Rotational Kinematics & Dynamics

A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5m. When released, it slips off the table in a very short time t = 0.01s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to :-

Show answer and solution

Answer: (d)

While slipping off, gravity gives a torque about the edge: $\alpha = \dfrac{mg(l/2)}{ml^2/3} = \dfrac{3g}{2l}$ .
Angular speed gained: $\omega = \alpha t = \dfrac{3 \times 10 \times 0.01}{2 \times 0.3} = 0.5$ rad/s.
Fall time: $t' = \sqrt{2h/g} = \sqrt{2 \times 5/10} = 1$ s.
$\theta = \omega t' = 0.5 \times 1 = 0.5$ rad, so the answer is (d).

Report a mistake

More questions on Rotational Kinematics & Dynamics

Two masses m and m/2 are connected at the two ends of a massless rigid rod of length l…JEE Main 2019 (9 Jan, Shift 1)
A uniform rod of length is being rotated in a horizontal plane with a constant angular…JEE Main 2019 (12 Apr, Shift 1)
A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the…NEET 2017
A uniform disc of radius R and mass M is free to rotate only about its axis. A string is…JEE Main 2017 (8 Apr, Shift 1)
A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is…NEET 2016 (Phase 1)
A roller is made by joining together two cones at their vertices O. It is kept on two…JEE Main 2016
A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of…JEE Main 2015 (11 Apr, Shift 1)
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal…NEET 2014 (AIPMT)

Rotational Kinematics & Dynamics question from JEE Main 2019 (8 Apr, Shift 2)

More questions on Rotational Kinematics & Dynamics