A uniform rod of mass 'm' and length 'l' lying on a smooth horizontal table is pivoted about one end. An impulse 'J' is applied to the other end. Angular speed with which rod starts rotating is

Question

A uniform rod of mass 'm' and length 'l' lying on a smooth horizontal table is pivoted about one end. An impulse 'J' is applied to the other end. Angular speed with which rod starts rotating is (A) (3 J/m l) (B) (3 J l/m) (C) (2 J/m l) (D) (2 J l/m)

Tardigrade Admin · Accepted Answer

Angular impulse =I(w2 - w1) ⇒ J× l=(m l2/3)(w - 0)⇒ w=(3 J/m l)

Q. A uniform rod of mass $^{'} m^{'}$ and length $^{'} l^{'}$ lying on a smooth horizontal table is pivoted about one end. An impulse $^{'} J^{'}$ is applied to the other end. Angular speed with which rod starts rotating is

$\frac{3 J}{m l}$

$\frac{3 J l}{m}$

$\frac{2 J}{m l}$

$\frac{2 J l}{m}$

Angular impulse $= I (w_{2} - w_{1})$
$\Rightarrow J \times l = \frac{m l ^{2}}{3} (w - 0) \Rightarrow w = \frac{3 J}{m l}$

Q. A uniform rod of mass ′m′ and length ′l′ lying on a smooth horizontal table is pivoted about one end. An impulse ′J′ is applied to the other end. Angular speed with which rod starts rotating is

ml3J​

m3Jl​

ml2J​

m2Jl​