A mass m slides from rest down the surface of a frictionless hemispherical bowl of radius r from the highest point A. The velocity of mass when it reaches the bottom is

Question

A mass m slides from rest down the surface of a frictionless hemispherical bowl of radius r from the highest point A. The velocity of mass when it reaches the bottom is (A)  √2gr  (B)  √mgr  (C) 2mgr (D)  gr

Tardigrade Admin · Accepted Answer

From the condition m g r=(1/2) m v2 ⇒ 2 g r=v2 ⇒ v=√2 g r

Q. A mass $m$ slides from rest down the surface of a frictionless hemispherical bowl of radius $r$ from the highest point $A$ . The velocity of mass when it reaches the bottom is

$2 g r$

$m g r$

$2 m g r$

$g r$

From the condition $m g r = \frac{1}{2} m v^{2}$
$\Rightarrow 2 g r = v^{2}$
$\Rightarrow v = 2 g r$

Q. A mass m slides from rest down the surface of a frictionless hemispherical bowl of radius r from the highest point A. The velocity of mass when it reaches the bottom is

2gr​

mgr​

2mgr

gr