A ball of mass 1 kg is suspended by an inextensible string 1 m long attached to a point O of a smooth horizontal bar resting on fixed smooth supports A and B. The ball is released from rest from the mass of the bar is 4 kg. The displacement of bar when ball reaches the other extreme position (in m) is

0.2
0.25
0.5
0.4

Question

A ball of mass 1 kg is suspended by an inextensible string 1 m long attached to a point O of a smooth horizontal bar resting on fixed smooth supports A and B. The ball is released from rest from the mass of the bar is 4 kg. The displacement of bar when ball reaches the other extreme position (in m) is

0.2
0.25
0.5
0.4

Toppr Admin · Accepted Answer

Here-Energy stored in-xA0-pendulum - work done on block-x2234-Mg-xD7-sp-mg-xD7-sbDisplacement-sb-xsp-2Lsin30-1Relative displacement-sp-1-x2212-xThus-M-x-m-1-x2212-x-4x-1-x2212-x-x2234-x-0-2 m

Here,Energy stored in pendulum = work done on block∴Mg×sp=mg×sbDisplacement,sb=xsp=2Lsin30=1Relative displacement,sp=1−xThus,M(x)=m(1−x)4x=1−x∴x=0.2 m

Here,
Energy stored in pendulum = work done on block
$∴ M g \times s_{p} = m g \times s_{b}$
Displacement,
$s_{b} = x$
$s_{p} = 2 L s i n 30 = 1$
Relative displacement,
$s_{p} = 1 - x$
Thus,
$M (x) = m (1 - x)$
$4 x = 1 - x$
$∴ x = 0.2$ m