1
JEE Main 2025 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination $45^{\circ}$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

A
$\sqrt{2} \mathrm{~g}$
B
$\frac{1}{\sqrt{2}} \mathrm{~g}$
C
$\frac{1}{3 \sqrt{2}} \mathrm{~g}$
D
$\frac{\sqrt{2} g}{3}$
2
JEE Main 2025 (Online) 23rd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $\theta(t)=5 t^2-8 t$, where $\theta(t)$ is the angular position of the rotating disc as a function of time $t$. How much power is delivered by the applied torque, when $t=2 \mathrm{~s}$ ?

A
$60 \mathrm{MR}^2$
B
$72 \mathrm{MR}^2$
C
$8 \mathrm{MR}^2$
D
$108 \mathrm{MR}^2$
3
JEE Main 2025 (Online) 23rd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A solid sphere of mass ' $m$ ' and radius ' $r$ ' is allowed to roll without slipping from the highest point of an inclined plane of length ' $L$ ' and makes an angle $30^{\circ}$ with the horizontal. The speed of the particle at the bottom of the plane is $v_1$. If the angle of inclination is increased to $45^{\circ}$ while keeping $L$ constant. Then the new speed of the sphere at the bottom of the plane is $v_2$. The ratio $v_1^2: v_2^2$ is

A
$1: 3$
B
$1: 2$
C
$1: \sqrt{2}$
D
$1: \sqrt{3}$
4
JEE Main 2025 (Online) 22nd January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i}+\hat{j}+\hat{k})$, would be

A
$\hat{j}+\hat{k}$
B
$\hat{i}-\hat{k}$
C
$\hat{i}-\hat{j}+\hat{k}$
D
$\hat{i}+\hat{k}$
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