A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

Question

A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be : (A) (g/2l) (B) (7g/3l) (C) (g/13l) (D) (g/3l)

Tardigrade Admin · Accepted Answer

Applying torque equation about point P. 2M0 (2l)-5 M0 gl = Iα I = 2M0(2l)2 + 5M0 l2 = 13 M0 l2d ∴ α = - (M0g ℓ/13M0 ℓ2) ⇒ α = - (g/13ℓ) ∴ α = (g/13ℓ) anticlockwise

Q. A rigid massless rod of length $3 l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

$\frac{g}{2 l}$

$\frac{7 g}{3 l}$

$\frac{g}{13 l}$

$\frac{g}{3 l}$

Applying torque equation about point P.
$2 M_{0} (2 l) - 5 M_{0} g l = I α$
$I = 2 M_{0} (2 l)^{2} + 5 M_{0} l^{2} = 13 M_{0} l^{2} d$
$∴ α = - \frac{M _{0} g ℓ}{13 M _{0} ℓ ^{2}} \Rightarrow α = - \frac{g}{13 ℓ}$
$∴ α = \frac{g}{13 ℓ}$ anticlockwise

Q. A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

2lg​

3l7g​

13lg​

3lg​