JEE Main 2022 · 26 Jun · Shift 1 · Physics Q34 · Dronacharya Exams

My attemptsTake a paper

← JEE Main 2022 · 26 Jun · Shift 1

PhysicsSingle correct+4 / -1Question 34 of 90

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 $\alpha$ with respect to point P. Which of the following graphs represent the correct relation between A and $\alpha$ when ball goes from Q to R ?

Cross-section of a hemispherical bowl with centre O on the horizontal rim line; P is the left rim point, Q a point on the bowl at angle α below OP, and R a lower point on the bowl.

A

A decreasing curve of A against

\alpha

, falling steeply then levelling off

A against α: decreasing curve, falling and flattening.

B

An increasing curve of A against

\alpha

, rising and levelling off

A against α: increasing curve rising from the origin and levelling off.

C

A horizontal line: A constant as

\alpha

varies

A against α: horizontal straight line.

D

A curve of A against

\alpha

, flat at first then falling to zero

A against α: starts at a constant level then curves down to zero.

Answer and worked solution

Official answer: C

Speed. Starting at rim level, after falling $R\sin\alpha$ : $v^2=2gR\sin\alpha$ .

Normal reaction. $N-mg\sin\alpha=\dfrac{mv^2}R=2mg\sin\alpha$ , so $N=3mg\sin\alpha$ .

Ratio. $A=\dfrac{2mg\sin\alpha}{3mg\sin\alpha}=\dfrac23$ , a constant: a horizontal line.

(C)

Topics:Motion in a vertical circle Circular motion dynamics

← Previous question Next question →