Question

A gramophone disc rotates with an uniform angular velocity of $6\text{rad/sec}$. A coin of mass $2\text{gm}$ is placed $5\text{cm}$ from the centre. The centripetal force acting on the coin is

• A. $3.6\times {10}^{-4}\text{N}$
• B. $3.6\times {10}^{-9}\text{N}$
• C. $3.6\times {10}^{-3}\text{N}$
• D. $3.6\times {10}^{-5}\text{N}$

Answer 1

The correct option is C $3.6\times {10}^{-3}\text{N}$

Given mass of coin $\left(m\right)=2\text{grams}=2\times {10}^{-3}\text{kg}$,
$r=5\text{cm}=5\times {10}^{-2}\text{m}$,
Angular speed $\left(\omega \right)=6\text{rad/s}$

Hence the centripetal force acting on the coin will be,
$F_c=m{\omega }^{2}r$
$\Rightarrow F_c=2\times {10}^{-3}\times 6^2\times 5\times {10}^{-2}$
$\Rightarrow F_c=3.6\times {10}^{-3}\text{N}$

Hence option C is the correct answer