A particle P is sliding down a frictionless hemispherical bowl. It passes point A at t=0 . At this instant of time, the horizontal component of its velocity is v . A bead Q of the same mass as P is ejected from A at t=0 along the horizontal string AB , with the speed v . Friction between the bead and the string may be neglected. Let tp and tQ be the, respective, times taken by P and Q to reach the point B . Then

Question

A particle P is sliding down a frictionless hemispherical bowl. It passes point A at t=0 . At this instant of time, the horizontal component of its velocity is v . A bead Q of the same mass as P is ejected from A at t=0 along the horizontal string AB , with the speed v . Friction between the bead and the string may be neglected. Let tp and tQ be the, respective, times taken by P and Q to reach the point B . Then Question

(A) tP < tQ (B) tP=tQ (C) tP>tQ (D) none of these

Tardigrade Admin · Accepted Answer

For particle P , motion between AC will be an accelerated one while between CB , a retarded one. But in any case, the horizontal component of its velocity will be greater than or equal to v . On the other hand, in the case of particle Q , it is always equal to v . Horizontal displacement for both the particles is equal. Therefore, tP < tQ .

$t_{P} < t_{Q}$

$t_{P} = t_{Q}$

$t_{P} > t_{Q}$

none of these

tP​<tQ​

tP​=tQ​

tP​>tQ​

none of these

$t_{P} < t_{Q}$

$t_{P} = t_{Q}$

$t_{P} > t_{Q}$