1
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$ . Its angular momentum, with respect to the origin, at time t = 2 is
A
36 $$\widehat k$$
B
- 48 $$\widehat k$$
C
$$- 34\left( {\widehat k - \widehat i} \right)$$
D
$$48\left( {\widehat i + \widehat j} \right)$$
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
A thin disc of mass M and radius R has mass per unit area $$\sigma$$(r) = kr2 where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :
A
$${{M{R^2}} \over 3}$$
B
$${{M{R^2}} \over 6}$$
C
$${{2M{R^2}} \over 3}$$
D
$${{M{R^2}} \over 2}$$
3
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
Two coaxial discs, having moments of inertia I1 and I1/2, are rotating with respective angular velocities $$\omega$$1 and $$\omega$$1/2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If Ef and Ei are the final and initial total energies, then (Ef - Ei) is:
A
$${{{I_1}\omega _1^2} \over {24}}$$
B
$${{{I_1}\omega _1^2} \over {12}}$$
C
$${3 \over 8}{I_1}\omega _1^2$$
D
$${{{I_1}\omega _1^2} \over {6}}$$
4
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
A particle of mass m is moving along a trajectory given by
x = x0 + a cos$$\omega$$1t
y = y0 + b sin$$\omega$$2t
The torque, acting on the particle about the origin, at t = 0 is :
A
Zero
B
+my0a $$\omega _1^2$$$$\widehat k$$
C
$$- m\left( {{x_0}b\omega _2^2 - {y_0}a\omega _1^2} \right)\widehat k$$
D
m (–x0b + y0a) $$\omega _1^2$$$$\widehat k$$
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