Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest, the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is _______ ${kg·m}^{2}$ .

$(g = 9.8 {m/s}^{2})$ [2026]

Question

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest, the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is _______ ${kg·m}^{2}$ .

$(g = 9.8 {m/s}^{2})$ [2026]

Smart Achievers · Accepted Answer

(3)

$S = u t + \frac{1}{2} a t^{2}$

$a = \frac{2 s}{t^{2}} = \frac{2 \times 0.81}{81} = 0.02 {m/s}^{2}$

$m_{1} g - T_{1} = m_{1} a$

$T_{2} - m_{2} g = m_{2} a$

$(T_{1} - T_{2}) R = I \cdot \frac{a}{R}$

$∴$ $a = \frac{(m_{1} - m_{2}) g}{m_{1} + m_{2} + \frac{I}{R^{2}}}$

$0.02 = \frac{(400 - 350) (10^{- 3}) g}{(400 + 350) (10^{- 3}) + \frac{I}{R^{2}}}$

$\frac{I}{R^{2}} = \frac{50 \times 10^{- 3} g}{0.02} - 750 \times 10^{- 3} = 23.75$

$I = 23.75 \times 4 \times 10^{- 4} = 9.5 \times 10^{- 3} {kg m}^{2}$

Solution

Q.
Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest, the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is _______ ${kg·m}^{2}$ .

$(g = 9.8 {m/s}^{2})$ [2026]

1 $4.75 \times 10^{- 3}$

2 $8.3 \times 10^{- 3}$

3 $9.5 \times 10^{- 3}$

4 $1.86 \times 10^{- 2}$

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Solution

Q. Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest, the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is _______ kg·m2. (g=9.8 m/s2) [2026]

1 4.75×10-3

2 8.3×10-3

3 9.5×10-3

4 1.86×10-2