1
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1

A disc is rolling without slipping on a surface. The radius of the disc is $$R$$. At $$t=0$$, the top most point on the disc is $$\mathrm{A}$$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

A
$$R\sqrt {({\pi ^2} + 1)}$$
B
$$2R$$
C
$$R\sqrt {({\pi ^2} + 4)}$$
D
$$2R\sqrt {(1 + 4{\pi ^2})}$$
2
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A : An electric fan continues to rotate for some time after the current is switched off.

Reason R : Fan continues to rotate due to inertia of motion.

In the light of above statements, choose the most appropriate answer from the options given below.

A
A is not correct but R is correct
B
A is correct but R is not correct
C
Both A and R are correct and R is the correct explanation of A
D
Both A and R are correct but R is NOT the correct explanation of A
3
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1

The torque of a force $$5 \hat{i}+3 \hat{j}-7 \hat{k}$$ about the origin is $$\tau$$. If the force acts on a particle whose position vector is $$2 i+2 j+k$$, then the value of $$\tau$$ will be

A
$$11 \hat{i}+19 \hat{j}-4 \hat{k}$$
B
$$-11 \hat{i}+9 \hat{j}-16 \hat{k}$$
C
$$-17 \hat{i}+19 \hat{j}-4 \hat{k}$$
D
$$17 \hat{i}+9 \hat{j}+16 \hat{k}$$
4
JEE Main 2022 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1

A solid cylinder and a solid sphere, having same mass $$M$$ and radius $$R$$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

A
$$\sqrt{\frac{5}{3}}$$
B
$$\sqrt{\frac{4}{5}}$$
C
$$\sqrt{\frac{3}{5}}$$
D
$$\sqrt{\frac{14}{15}}$$
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