A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R ?

Question

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

V=√2 g R sin α N-m g sin α=(m v2/R)=2 m g sin α

( N /2 mg sin α)=(1/2)+1=(3/2)

⇒ A = constant

V=2gRsinα​ N−mgsinα=Rmv2​=2mgsinα 2mgsinαN​=21​+1=23​ ⇒A= constant

$V = 2 g R sin α$
$N - m g sin α = \frac{m v ^{2}}{R} = 2 m g sin α$

$\frac{N}{2 m g s i n α} = \frac{1}{2} + 1 = \frac{3}{2}$

$\Rightarrow A =$ constant