1.

A current-carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it.The correct statement(s) is(are)

A) The emf induced in the Ioop is zero if the current is constant

B) The emf induced in the loop is finite if the current is constant

C) The emf induced in the loop is zero if the current decreases at a steady rate

D) The emf induced in the loop is finite if the current decreases at a steady rate

2.

In the given circuit, the AC source has $\omega$ = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

A) the current through the circuit ,I is 0.3 A

B) The current through the circuit ,l is $0.3 \sqrt{2}A$

C) The voltage across 100$\Omega$ resistor = $10 \sqrt{2}$

D) the voltage across $50 \Omega$ resistor =10V

3.

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed $\omega/2$. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a

distance R from the origin, where OP makes an angle of $30^{0}$ with the horizontal. Then with respect to the horizontal surface.

A) the point O has a linear velocity $3 R\omega i$

B) the point P has a linear velocity $\frac{11}{4} R \omega i-\frac{\sqrt{3}}{4}R\omega k$

C) the point P has a linear velocity $\frac{13}{4} R \omega i-\frac{\sqrt{3}}{4}R\omega k$

D) the point P has a linear velocity $ \left(3-\frac{\sqrt{3}}{4}\right)R\omega i+\frac{1}{4}R \omega k$

4.

Two spherical planets P and Q have the same uniform density P, masses Mp and M_{Q}, and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is (M_{P} + M_{Q}). The escape velocities from the planets P, Q and R, are V_{P, }V_{Q, and }V_{R}, respectively. Then

A) $V_{Q} $ >$V_{R}$ > $V_{P}$

B) $V_{R}$ >$V_{Q}>$$V_{P}$

C) $V_{R}/V_{P}$=3

D) $V_{P}/V_{Q}=\frac{1}{2}$

5.

Two solid cylinders P and Q of the same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

A) Both cylinders P and Q reach the ground at the same time

B) Cylinder P has larger linear acceleration than cylinder Q

C) Both cylinders reach the ground with same transiational kinetic energy

D) Cylinder Q reaches the ground with larger angular speed

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