First slide

Torque

Question

A wheel and an axle is made to rotate about a horizontal axis with the help of a body of mass 5 kg attached to a string wound around the axle. The radius of the axle is l0 cm. The body falls vertically through 5 m in 10 s starting from rest. The moment of inertia of the wheel and axle is :

Moderate

A

3.85 kg m²
B

4.85 kg m²
C

5.85 kg m²
D

2.85 kg m²

Solution

$a_{0} = \frac{5 g}{5 + \frac{I}{R^{2}}}$
From $s = ut + \frac{1}{2} {at}^{2}$
$a = \frac{2 s}{t^{2}} = \frac{2 \times 5}{10^{2}} = \frac{1}{10}$
$So, \frac{1}{10} = \frac{5 g}{5 + \frac{I}{(0 .1)^{2}}} \Rightarrow 5 + \frac{I}{(0 .1)^{2}} = 50 g$
So, I = 485 x 10^-2 = 4.85kg-m²

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