JEE Main Rotational Motion PYQ

11. (JEE Main 2022 (Online) 29th June Morning Shift)

A spherical shell of 1 kg mass and radius R is rolling with angular speed $ω$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is $\frac{a}{3}$ R² $ω$ . The value of a will be :

JEE Main 2022 (Online) 29th June Morning Shift Physics - Rotational Motion Question 47 English

A. 2

B. 3

C. 5

D. 4

Correct Answer is Option (C)

${\vec{L}}_{0} = {\vec{L}}_{o f c m} + {\vec{L}}_{a b o u t c m}$

$\Rightarrow \frac{a}{3} R^{2} ω = m v R + \frac{2}{3} m R^{2} ω = \frac{5}{3} m R^{2} ω$

$\Rightarrow a = 5$

12. (JEE Main 2022 (Online) 26th June Morning Shift)

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads^{$-$ 1} in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads^{$-$ 1}).

A. $\frac{M}{(M + m)}$

B. $\frac{(M + 2 m)}{2 M}$

C. $\frac{2 M}{(M + 2 m)}$

D. $\frac{2 (M + 2 m)}{M}$

Correct Answer is Option (C)

$I_{1} ω_{1} = I_{2} ω_{2}$

$M R^{2} ω_{1} = (M R^{2} + 2 m R^{2}) ω_{2}$

$ω_{2} = (\frac{M}{M + 2 m}) ω_{1}$

$ω_{2} = 2 (\frac{M}{M + 2 m})$

13. (JEE Main 2022 (Online) 28th June Morning Shift )

The position vector of 1 kg object is $\vec{r} = (3 \hat{i} - \hat{j}) m$ and its velocity $\vec{v} = (3 \hat{j} + \hat{k}) m s^{- 1}$ . The magnitude of its angular momentum is $\sqrt{x}$ Nm where x is ___________.

Correct answer is (91)

$| \vec{i} | = | \vec{r} \times (m \vec{v}) |$

$= | (3 \hat{i} - \hat{j}) \times (3 \hat{j} + \hat{k}) |$

$= | - \hat{i} - 3 \hat{j} + 9 \hat{k} |$

$= \sqrt{91}$

14. (JEE Main 2021 (Online) 31st August Morning Shift)

Angular momentum of a single particle moving with constant speed along circular path :

A. changes in magnitude but remains same in the direction

B. remains same in magnitude and direction

C. remains same in magnitude but changes in the direction

D. is zero

Correct Answer is Option (B)

JEE Main 2021 (Online) 31st August Morning Shift Physics - Rotational Motion Question 50 English Explanation
$| \vec{L} |$ = mvr

And direction will be upward & remain constant.

Option (b)

15. (JEE Main 2021 (Online) 27th August Evening Shift)

Two discs have moments of inertia I₁ and I₂ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $ω$ ₁ and $ω$ ₂ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

A. $\frac{I_{1} I_{2}}{(I_{1} + I_{2})} (ω_{1} - ω_{2})^{2}$

B. $\frac{{(I_{1} - I_{2})}^{2} ω_{1} ω_{2}}{2 (I_{1} + I_{2})}$

C. $\frac{I_{1} I_{2}}{2 (I_{1} + I_{2})} (ω_{1} - ω_{2})^{2}$

D. $\frac{{(ω_{1} - ω_{2})}^{2}}{2 (I_{1} + I_{2})}$

Correct Answer is Option ()