Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20249 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Evening Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2024 · 9 April · Evening Shift · Physics · Rotational Motion

A circular disc reaches from top to bottom of an inclined plane of...

A circular disc reaches from top to bottom of an inclined plane of length ll. When it slips down the plane, if takes t st \mathrm{~s}. When it rolls down the plane then it takes \left(\frac{\alpha}{2}\right)^{1 / 2} t \mathrm{~s},where, where\alpha is _________

Correct answer

0

Step-by-step solution

For slipping a=gsin⁡θℓ=12at2⇒t=2ℓgsin⁡θ\begin{aligned}& \mathrm{a}=\mathrm{g} \sin \theta \\ & \ell=\frac{1}{2} \mathrm{at}^2 \Rightarrow \mathrm{t}=\sqrt{\frac{2 \ell}{\mathrm{g} \sin \theta}}\end{aligned} For rolling a′=gsin⁡θ1+k2R2[k=R2]&⇒a′=2 gsin⁡θ3&ℓ=12a′(t′)2&⇒t′=6ℓ2 gsin⁡θ=α22ℓgsin⁡θ⇒α=3\begin{aligned}& \mathrm{a}^{\prime}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{k}^2}{\mathrm{R}^2}}\left[\mathrm{k}=\frac{\mathrm{R}}{\sqrt{2}}\right] \& \Rightarrow \mathrm{a}^{\prime}=\frac{2 \mathrm{~g} \sin \theta}{3} \& \ell=\frac{1}{2} \mathrm{a}^{\prime}\left(\mathrm{t}^{\prime}\right)^2 \& \Rightarrow \mathrm{t}^{\prime}=\sqrt{\frac{6 \ell}{2 \mathrm{~g} \sin \theta}}=\sqrt{\frac{\alpha}{2}} \sqrt{\frac{2 \ell}{\mathrm{g} \sin \theta}} \\ & \Rightarrow \alpha=3\end{aligned}
Practice Rotational Motion on Quantrex Academy →

More from Rotational Motion

Consider a large disk of radius R and two smaller disks, each of radius r = R/50 , lying… JEE Advanced 2026A solid cylinder of radius R rolls without slipping with a center of mass speed v_0 =… JEE Advanced 2026List-I shows four planar structures made of uniform solid rods each of mass m and length… JEE Advanced 2026Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top… JEE Advanced 2026Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top… JEE Advanced 2026A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At… JEE Main 2026A solid sphere ( A ) of mass 5m and a spherical shell ( B ) of mass m , both having same… JEE Main 2026A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through… JEE Main 2026 Full Rotational Motion list All JEE Main PYQs