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.

Answer 1

The Correct Option is C

\(N=mg\ sin\ α+ \frac {mv^2}{r}\)
and, \(v^2 = 2g × R\ sin\ α\)
\(∴N = mg\ sin\ α + m × (2g\ sin\ α)\)
\(= 3mg\ sin\ α\)
∴ratio, \(A=\frac {\frac {mv^2}{R}}{N}\)
\(=\frac {2mg\ sin\ α}{3mg\ sin\ α}\)

\(=\frac {2}{3}\)

So,the corrct option is \((C)\):