Single Choice

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

A10cm/s,10cm/s2
Correct Answer
B10cm/s,80cm/s2
C40cm/s,10cm/s2
D40cm/s,40cm/s2

Solution

Velocity of the particle in circular motion is equal to w.r, so if w is constant the velocity is proportional to r. Here the particle is kept at the half radius. $$\therefore$$ Velocity will be half i.e., $$10 \dfrac{m}{s}$$.

Similarly, acceleration is $${ w }^{ 2 }r$$, here too $${ w }^{ 2 }$$ is constant. So acceleration is also proportional to ‘r’.

Making radius half will make acceleration half i.e. $$10{ cm }/{ { s }^{ 2 } }$$

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