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System of Particles and Rotational Motion

Angular displacement, angular velocity, angular acceleration

A rigid massless rod of length 3 l has two masses attached at

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Solving time: 4 mins

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

(a) $\frac{g}{13 l}$
(b) $\frac{g}{2 l}$
(c) $\frac{7 g}{3 l}$
(d) $\frac{g}{3 l}$

Name: Video solution 1: 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) 13lg(b) 2lg(c) 3l7g(d) 3lg
Uploaded: 2023-01-15T11:28:45.000Z
Duration: 7 min
Description: Video solution 1: 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) 13lg(b) 2lg(c) 3l7g(d) 3lg

Views: 6,191 students

Updated on: Jan 15, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2019

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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

(a)

\frac{g}{13 l}

(b)

\frac{g}{2 l}

(c)

\frac{7 g}{3 l}

(d)

\frac{g}{3 l}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Exp. (a)
Key Idea When a rod is pivoted at any point, its angular acceleration is given by

τ_{n e t} =∣ α

.

The given condition can be drawn in the figure below
Solution Image

Torque

(τ)

about

P = r_{1} \times F_{1} + r_{2} \times F_{2} \dots (i)

\Rightarrow τ = I \times 5 M_{0} g

(outwards)

- 2 I \times 2 M_{0} g

(inwards)

\Rightarrow τ = 5 M_{0} g I - 4 M_{0} g l

(outwards)

\Rightarrow τ = M_{0} g l

(outwards)
or

τ = M_{0} g I \dots (ii)

Now we know that, torque is also given by

τ = l α \dots (iii)

Here, I = moment of inertia (w.r.t. point

P

) of rod and

α =

angular acceleration.
For point

P, I = (5 M_{0}) \times I^{2} + (2 M_{0}) (2 I)^{2}

[∵ I = M R^{2}] \dots (i v)

Putting value of I from Eq. (iv) in Eq. (iii), we get

τ = (13 M_{0} I^{2}) α \dots (v)

From Eqs. (ii) and (v), we get

M_{0} g l = 13 M_{0} I^{2} α

\Rightarrow α = \frac{g}{13 I}

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Question Text	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 (a) $\frac{g}{13 l}$ (b) $\frac{g}{2 l}$ (c) $\frac{7 g}{3 l}$ (d) $\frac{g}{3 l}$
Updated On	Jan 15, 2023
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	161
Avg. Video Duration	7 min

Text solutionVerified

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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) 13lg​(b) 2lg​(c) 3l7g​(d) 3lg​

Text solutionVerified

Filo tutor solutions (1)

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