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 5 m . When released, it slips off the table in a very short time τ = 0.01 s , re

Question

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 5 m . When released, it slips off the table in a very short time τ = 0.01 s , remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:

TestHub · Accepted Answer

Angular impulse = change in angular momentum
$τ Δ t = Δ L$
$m g \frac{l}{2} \times 0.01 = \frac{m l^{2}}{3} ω$
$ω = \frac{3 g \times 0.01}{2 l} = \frac{3 \times 10 \times 0.01}{2 \times 0.3} = 0.5 r a d / s e c$
Time taken by rod to hit the ground = $\sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \times 5}{10}} = 1 s$
Angle rotated by rod = $ω t = 0.5 \times 1 = 0.5 r a d$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion