Question

A particle is kept fixed on a turntable rotating uniformly. As seen from the ground, the particle goes in a circle, its speed is $20 \,cm / s$ and acceleration is $20\, cm / s ^{2}$. The particle is now shifted to a new position to make the radius half of the original value. The new values of the speed and acceleration will be :

• A. $10 \,cm / s , 10 \,cm / s ^{2}$
• B. $10\, cm / s , 80\, cm / s ^{2}$
• C. $40\, cm / s , 10\, cm / s ^{2}$
• D. $40 \,cm / s , 40\, cm / s ^{2}$.

Answer 1

Answer: (A)

The angular velocity and angular acceleration remains constant :
$\Rightarrow \frac{v}{r} =\frac{v^{\prime}}{r^{\prime}}\,\,\,\,(v=\omega r)$
$\frac{20}{r} =\frac{v^{\prime}}{r / 2}$
$v^{\prime} =10\, cm / s$
Similarly, $ \frac{a}{r} =\frac{a^{\prime}}{r^{\prime}} $
$\frac{20}{r} =\frac{a^{\prime}}{r / 2}$
$a^{\prime}=10\, cm / s ^{2}$