First slide

Rotational motion

Question

Find the acceleration of the body if a force F - 8 N pulls the string at P that passes over the body and it is connected by another string to a rigid support at Q.(Take radius of
gyration $k = \frac{2}{\sqrt{3}} m, R = 2 m, r = 1 m$ and mass of the body m=3 kg)

Moderate

A

$1 m / s^{2}$
B

$1.5 m / s^{2}$
C

$1.2 m / s^{2}$
D

$2 m / s^{2}$

Solution

$\begin{array}{l} a = α R \\ F - T = m a . . . . . . . (i) \\ Torque about C: \\ T R - F r = I α \\ \Rightarrow T R - F r = m k^{2} \frac{a}{R} \end{array}$
Put the value of T from equation (i)
$\begin{array}{l} (F - m a) R - F r = \frac{m k^{2} a}{R} \\ F (R - r) = a [\frac{m k^{2}}{R} + m R] \Rightarrow a = \frac{F R (R - r)}{(k^{2} + R^{2}) m} \\ = \frac{8 \times 2 \times (2 - 1)}{(\frac{4}{3} + 4) \times 3} = \frac{8 \times 2 \times 1}{4 \times \frac{4}{3} \times 3} = 1 m / s^{2} \end{array}$

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