A uniform rod AB of mass 2 kg… - JEE Main 2024 Physics PYQ

JEE Main 2024 — Physics Mechanics

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A uniform rod $AB$ of mass $2\mathrm{kg}$ and Length $30\mathrm{cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2Ns$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi }{x}s,$ where $x=$ ____.

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Held on 1 Feb 2024 · Verified 6 Jul 2026.

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Solution

JEE Main 2024 Physics, Center of Mass Momentum and Collision — solution figure

Impulse $J=0.2Ns$

$\Rightarrow J=\int Fdt=0.2Ns$

Now, angular impulse $(\vec{M})$ will be

${M}_{c}=\int \tau dt$

$=\int F\frac{L}{2}dt$

$=\frac{L}{2}\int Fdt=\frac{L}{2}\times J$

$=\frac{0.3}{2}\times 0.2$

$=0.03$

Moment of inertia of the rod about the centre of mass, ${I}_{\mathrm{cm}}=\frac{M{L}^{2}}{12}=\frac{2\times (0.3{)}^{2}}{12}=\frac{0.09}{6}$

Angular impulse will be equal to the change in angular momentum.

$M={I}_{\mathrm{cm}}({\omega }_{f}-{\omega }_{i})$

$\Rightarrow 0.03=\frac{0.09}{6}({\omega }_{f})$

$\Rightarrow {\omega }_{f}=2\mathrm{rad}{s}^{-1}$

For angular displacement, we can write $\theta =\omega t$

$\Rightarrow t=\frac{\theta }{\omega }=\frac{\pi }{2\times 2}=\frac{\pi }{4}s$ .

Therefore, $x=4$ .

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Solution

JEE Main 2024 Physics, Center of Mass Momentum and Collision — solution figure

Impulse $J=0.2Ns$

$\Rightarrow J=\int Fdt=0.2Ns$

Now, angular impulse $(\vec{M})$ will be

${M}_{c}=\int \tau dt$

$=\int F\frac{L}{2}dt$

$=\frac{L}{2}\int Fdt=\frac{L}{2}\times J$

$=\frac{0.3}{2}\times 0.2$

$=0.03$

Moment of inertia of the rod about the centre of mass, ${I}_{\mathrm{cm}}=\frac{M{L}^{2}}{12}=\frac{2\times (0.3{)}^{2}}{12}=\frac{0.09}{6}$

Angular impulse will be equal to the change in angular momentum.

$M={I}_{\mathrm{cm}}({\omega }_{f}-{\omega }_{i})$

$\Rightarrow 0.03=\frac{0.09}{6}({\omega }_{f})$

$\Rightarrow {\omega }_{f}=2\mathrm{rad}{s}^{-1}$

For angular displacement, we can write $\theta =\omega t$

$\Rightarrow t=\frac{\theta }{\omega }=\frac{\pi }{2\times 2}=\frac{\pi }{4}s$ .

Therefore, $x=4$ .

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Solution

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Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics