Question

A particle of mass $1g$ executes an oscillatory motion on the concave surface of a spherical dish of radius $2m$ placed on a horizontal plane. If the motion of the particles starts from a point on the dish at a height of $1cm$ from the horizontal plane and the coefficient of friction is $0.01$, how much total distance will be moved by the particle before it comes to rest at the bottom of the concave surface?

• A. $100m$
• B. $1m$
• C. $10m$
• D. $0.1m$

Answer 1

The correct option is B $1m$

Loss in mechanical energy $=$ work done against friction
$mgh=\mu mg\cos \theta \times s$
$s=\frac{h}{\mu g\cos \theta }=\frac{1\times {10}^{-2}}{0.01\times 10\times \frac{2-h}{2}}=1.005m\approx 1m$