Ncert Exercises & Solutions

A mass of 5 kg is moving along a circular path of radius 1 m. If the mas moves with 300 rev/min, its kinetic energy would be

1. 250 $π^{2}$

2. 100 $π^{2}$

3. 5 $π^{2}$

4. 0

(a) Hint: Using angular velocity, we can find the linear speed.

Step 1: Find the angular speed of the mass.

$Given, mass = m = 5 kg$
$Radius = 1 m = R$
$Revolution per \min . ω = 300 rev / \min$
$= (300 \times 2 π) rad / \min$
$= (300 \times 2 \times 3 .14) rad / 60 s$
$= \frac{300 \times 2 \times 3 .14}{60} rad / s = 10 πrad / s$

Step 2: Find the kinetic energy of the mass.

$\begin{array}{l} ⇒ linear speed = v = ωR \\ = (\frac{300 \times 2 π}{60}) (1) \\ = 10 πm / s \\ KE = \frac{1}{2} {mv}^{2} \\ = \frac{1}{2} \times 5 \times (10 π)^{2} \\ = 100 π^{2} \times 5 \times \frac{1}{2} \\ = 250 π^{2} J \end{array}$

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