Question:medium

A uniform rod of mass 20 kg and length 1.6 m is pivoted at its one end and can swing freely in the vertical plane. The angular acceleration of the rod just after the rod is released from rest in the horizontal position is:

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Angular acceleration for a pivoted rod depends on the length; longer rods have lower angular acceleration.
Updated On: Jun 10, 2026
  • $\frac{15}{16}g$
  • $\frac{17}{16}g$
  • $\frac{16}{15}g$
  • $\frac{9}{16}g$
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The Correct Option is A

Solution and Explanation

Step 1: Picture the rod.
A uniform rod of mass 20 kg and length $L = 1.6$ m is hinged at one end and held horizontal. When released, gravity makes it swing down. We want the angular acceleration right at the start.

Step 2: Recall the rotation rule.
For rotation, torque equals moment of inertia times angular acceleration: $\tau = I \alpha$. So $\alpha = \tau / I$.

Step 3: Find the torque from gravity.
Gravity acts at the rod's centre, a distance $L/2$ from the hinge. So the turning torque is $\tau = M g \times \dfrac{L}{2}$.

Step 4: Write the moment of inertia.
For a rod pivoted at one end, $I = \dfrac{M L^{2}}{3}$.

Step 5: Combine to find angular acceleration.
$\alpha = \dfrac{M g (L/2)}{M L^{2}/3} = \dfrac{3 g}{2 L}$. The mass cancels out, which is a neat check.

Step 6: Put in the length.
With $L = 1.6$ m: $\alpha = \dfrac{3 g}{2 \times 1.6} = \dfrac{3 g}{3.2} = \dfrac{15}{16} g$. \[ \boxed{\dfrac{15}{16} g} \]
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