Question

Q. 15 & 7 (system of particles, Normal Reaction, work Energy Theorem)
1. A ball of mass m and radius r is released from rest inside a hollow smooth sphere of mass m and radius R as shown in figure. The horizontal surface is smooth. The normal reaction on the ball when it reaches the lowest position is (r << R)

• A. 2 mg
• B. 3 mg
• C. 4 mg
• D. 5 mg

Answer 1

The correct option is B 3 mg

R.E.F image

Solution

From $A-B,W_{gravity}=mgR$

so by work - Energy Theorem,

$w_{net}=△$ KE

Here, $mgR=\frac{m{v}^2}{2}-\frac{m(0{)}^2}{2}$

$\Rightarrow 2mg=\frac{m{v}^2}{R}$

Also, N-mg = ma [second law of motion]

Here a $\to$ centripetal $a{u}^n=\frac{v^2}{R}$

$\Rightarrow N=\frac{m{v}^2}{R}+mg=2mg+mg=3mg$

Option - B is correct