Question

A ball of mass $1\text{kg}$ moves inside a smooth fixed spherical shell of radius $1\text{m}$ with an initial velocity $v=5\text{m/s}$ from the bottom. What is the total force acting on the particle at point $B$?

• A. $10\text{N}$
• B. $25\text{N}$
• C. $5\sqrt{5}\text{N}$
• D. $5\text{N}$

Answer 1

The correct option is C $5\sqrt{5}\text{N}$

Let speed of ball at $B$ be $v$
Kinetic energy at $A$,
$K_A=\frac{1}{2}\left(1\right)(5{)}^2=12.5\text{J}$
Applying Law Of Conservation of energy between $A$ and $B$
Taking $A$ as reference :
$K_A=U_B+K_B=mgr+K_B$
$\Rightarrow 12.5=\left(1\right)\left(10\right)\left(1\right)+\frac{1}{2}\left(1\right)v^2$
$\Rightarrow v^2=5$
Force acting on particle at $B$,
$F=\sqrt{(mg{)}^2+{\left(\frac{m{v}^2}{r}\right)}^2}$
$F=\sqrt{(10{)}^2+{\left(\frac{1\times 5}{1}\right)}^2}$
$=\sqrt{125}=5\sqrt{5}\text{N}$