JEE Main 2022 Question Paper (28-Jun-2022) (Shift 1)

Question 1

Assertion (A): Product of Pressure $\left(Pight)$ and time $\left(tight)$ has the same dimension as that of coefficient of viscosity. Reason (R): Coefficient of viscosity $= \frac{	ext{Force}}{	ext{Velocity gradient}}$

Accepted Answer

A is true but R is false.

Answer

Both A and R are true, and R is the correct explanation of A.

Answer

Both A and R are true but R is NOT the correct explanation of A.

Answer

A is false but R is true.

Question 2

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is varying with time $t$ as $ a_{c} = k^{2} r t^{2}, $ where $k$ is a constant. The power delivered to the particle by the force acting on it is -

Accepted Answer

$m k^{2} r^{2} t$

Answer

Zero

Answer

$2m k^{2} r^{2} t$

Answer

$2m k^{2} r t$

Question 3

Motion of a particle in the $x$-$y$ plane is described by the following set of equations: $ x = 4 \sin\left(\frac{\pi}{2} - \omega tight) \quad \mathrm{m} \quad 	ext{and} \quad y = 4 \sin(\omega t) \quad \mathrm{m}. $ The path of the particle will be

Accepted Answer

circular

Answer

helical

Answer

parabolic

Answer

elliptical

Question 4

Match List-I with List-II List-I List-II (A) Moment of inertia of solid sphere of radius $ R $ about any tangent. (I) $ \frac{5}{3} M R^{2} $ (B) Moment of inertia of hollow sphere of radius $ R $ about any tangent. (II) $ \frac{7}{5} M R^{2} $ (C) Moment of inertia of circular ring of radius $ R $ about its diameter. (III) $ \frac{1}{4} M R^{2} $ (D) Moment of inertia of circular disc of radius $ R $ about any diameter. (IV) $ \frac{1}{2} M R^{2} $

Accepted Answer

$ \mathrm{A} - \mathrm{II}, \quad \mathrm{B} - \mathrm{I}, \quad \mathrm{C} - \mathrm{IV}, \quad \mathrm{D} - \mathrm{III} $

Answer

$ \mathrm{A} - \mathrm{I}, \quad \mathrm{B} - \mathrm{II}, \quad \mathrm{C} - \mathrm{IV}, \quad \mathrm{D} - \mathrm{III} $

Answer

$ \mathrm{A} - \mathrm{II}, \quad \mathrm{B} - \mathrm{I}, \quad \mathrm{C} - \mathrm{III}, \quad \mathrm{D} - \mathrm{IV} $

Answer

$ \mathrm{A} - \mathrm{I}, \quad \mathrm{B} - \mathrm{II}, \quad \mathrm{C} - \mathrm{III}, \quad \mathrm{D} - \mathrm{IV} $

Question 5

Two planets $A$ and $B$ of equal mass have their periods of revolution $T_{A}$ and $T_{B}$ such that $T_{A} = 2 T_{B}$. These planets are revolving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which of the following would be the correct relationship between their orbits?

Accepted Answer

${r}_{A}^{3} = 4 {r}_{B}^{3}$

Answer

$2r_{A}^{2} = r_{B}^{3}$

Answer

${r}_{A}^{3} = 2 {r}_{B}^{3}$

Answer

${T}_{A}^{2} - {T}_{B}^{2} = \frac{\pi^{2}}{GM} \left( r_{B}^{3} - 4 r_{A}^{3} \right)$

	List-I		List-II
(A)	Moment of inertia of solid sphere of radius \( R \) about any tangent.	(I)	\( \frac{5}{3} M R^{2} \)
(B)	Moment of inertia of hollow sphere of radius \( R \) about any tangent.	(II)	\( \frac{7}{5} M R^{2} \)
(C)	Moment of inertia of circular ring of radius \( R \) about its diameter.	(III)	\( \frac{1}{4} M R^{2} \)
(D)	Moment of inertia of circular disc of radius \( R \) about any diameter.	(IV)	\( \frac{1}{2} M R^{2} \)