A block of mass m=1 kg slides… - JEE Main 2020 Physics PYQ

JEE Main 2020 — Physics Mechanics

2020mcqhard

A block of mass $m=1\mathrm{kg}$ slides with velocity $v=6m{s}^{-1}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $O$ and swings as a result of the collision making angle $\theta$ before momentarily coming to rest. if the rod has mass $M=2\mathrm{kg},$ and length $\ell =1m,$ the value of $\theta$ is approximately $(\mathrm{take}g=10m{s}^{-2})$

JEE Main 2020 Physics, Rotational Motion — question figure

Official previous-year question

Held on 3 Sept 2020 · Verified 6 Jul 2026.

Options

A
$63^{\circ}$
B
$55^{\circ}$
C
$69^{\circ}$
D
$49^{\circ}$

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Solution

Angular momentum

$\mathrm{mv}l=(m{l}^{2}+\frac{2m{l}^{2}}{3})\omega$

$\mathrm{mv}l=\frac{5}{3}m{l}^{2}\omega$

$\omega =\frac{3v}{5l}$

$\frac{1}{2}{I\omega }^{2}=2\mathrm{mg}\frac{l}{2}(1-\mathrm{cos}\theta )+\mathrm{mg}l(1-\mathrm{cos}\theta )$

$\frac{1}{2}(\frac{5}{3}m{l}^{2})\frac{9{v}^{2}}{25{l}^{2}}=2\mathrm{mg}l(1-\mathrm{cos}\theta )$

$\frac{3}{5\times 2}{\mathrm{mv}}^{2}=2\mathrm{mg}l(1-cos\theta )$

$\frac{3}{10}\times \frac{36}{2\times 10}=1-\mathrm{cos}\theta$

$1-\frac{27}{50}=\mathrm{cos}\theta$

$\mathrm{cos}\theta =\frac{23}{50}=0.46$

$\theta ={\mathrm{cos}}^{-1}(0.46)=63^{\circ}$

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Solution

Angular momentum

$\mathrm{mv}l=(m{l}^{2}+\frac{2m{l}^{2}}{3})\omega$

$\mathrm{mv}l=\frac{5}{3}m{l}^{2}\omega$

$\omega =\frac{3v}{5l}$

$\frac{1}{2}{I\omega }^{2}=2\mathrm{mg}\frac{l}{2}(1-\mathrm{cos}\theta )+\mathrm{mg}l(1-\mathrm{cos}\theta )$

$\frac{1}{2}(\frac{5}{3}m{l}^{2})\frac{9{v}^{2}}{25{l}^{2}}=2\mathrm{mg}l(1-\mathrm{cos}\theta )$

$\frac{3}{5\times 2}{\mathrm{mv}}^{2}=2\mathrm{mg}l(1-cos\theta )$

$\frac{3}{10}\times \frac{36}{2\times 10}=1-\mathrm{cos}\theta$

$1-\frac{27}{50}=\mathrm{cos}\theta$

$\mathrm{cos}\theta =\frac{23}{50}=0.46$

$\theta ={\mathrm{cos}}^{-1}(0.46)=63^{\circ}$

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Options

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