Newton's Ball!

Classical Mechanics Level 1

A spherical ball of mass $m$ is kept at the highest point in the space between two fixed concentric spheres $A$ and $B$ . The smaller sphere $A$ has a radius $R$ and the space between the two spheres has a width $d$ . The ball has a diameter very slightly less than $d$ . All surfaces are frictionless. The ball is given a gentle push towards the right . The angle made by the radius vector of the ball with the upward vertical is $\theta$ . What is the total normal reaction force exerted by the spheres on the ball in terms of angle $\theta$ ?

N=mg(2\cos\theta-3)

N=mg(3\sin\theta-2)

N=mg(3\tan\theta-2)

N=mg(3\cos\theta-2)

N=mg(2\sin\theta-3)

N=mg(2\tan\theta-3)

2 solutions

Gagan Raj
Apr 5, 2015

Velocity of the ball at angle $\theta$ is

Let $N$ be the normal reaction (away from the centre.....there is only one centre) at angle $\theta$ . Then...........

Substituting the value of $v^2$ ..... we get ......

This is my solution.....if anyone finds any error please feel free to correct me !!!!!

Enjoy And Learn !!!!!

In your initial equation for velocity, you substituted for $g$ instead of $h$ .

Nicholas Stearns - 6 years, 2 months ago

Oops.....thanks for the correction.....i'll change it immediately !!!!!

Gagan Raj - 6 years, 2 months ago

I don "t get it. If we see this setup from our frame of reference then centripetal force + mg cos@ must be added . Because they are in the same direction I.e inwards towards the centre.

Mukul Sharma - 5 years, 6 months ago

Samuel Li
Apr 5, 2015

Anti-Solution: When $\theta = 0$ , the normal force is simply $mg$ . Substituting $\theta = 0$ into all the given answer choices, we find that only $N = mg(3\cos{\theta}-2)$ gives $N = mg$ , so it must be the correct answer.

We cannot do like this it was a subjective question of iit 2002 so we cannot verify the option .

tony stark - 2 years, 1 month ago

Newton's Ball!

2 solutions

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