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 $t_{p}$ and $t_{Q}$ be the, respective, times taken by $P$ and $Q$ to reach the point $B$ . Then

• A. $t_{P} < t_{Q}$
• B. $t_{P}=t_{Q}$
• C. $t_{P}>t_{Q}$
• D. none of these

Answer 1

Answer: (A)

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, $t_{P} < t_{Q}$ .