The mass of a hydrogen molecule is 3.32 x 10^-27 kg. If 10²³ hydrogen molecules strike, per second, a fixed wall of area 2cm² at an angle of 45° to the normal, and rebound elastically with a speed of 10³ m/s, then the pressure on the wall is nearly:

• 4.70 x 10² N/m²

• 2.35 x 10³ N /m²

• 4.70 x 10³ N/m²

• 2.35 x 10² N /m²

A particle is moving in a circular path of radius a under the action of an attractive potential U = -k/2r². its total energy is:

• $-\frac{3}{2}\frac{k}{a^2}$

• $\frac{-k}{4a^2}$

• $\frac{k}{2a^2}$

• zero

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, −σ and +σ respectively. The potential of shell B is :

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:

• $\frac{181}{2}M{R}^2$

• $\frac{19}{2}\hspace{0.17em}M{R}^2$

• $\frac{55}{2} M{R}^2$

• $\frac{73}{2}M{R}^2$

15.

From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:

• $\frac{37}{9}M{R}^2$

• 4MR²

• $\frac{40}{9}M{R}^2$

• 10 MR²

The reading of the ammeter for a silicon diode in the given circuit is

• 13.5 mA

• 0 mA

• 15 mA

• 11.5 mA

For an RLC circuit driven with a voltage of amplitude v_m and frequency ${\omega }_0 = \frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by:

• $\frac{CR}{{\omega }_0}$

• $\frac{{\omega }_{0}L}{R}$

• $\frac{{\omega }_{0}R}{L}$

• $\frac{R}{\left({\omega }_{0}C\right)}$

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10Ω. The internal resistance of the two batteries are 1Ω and 2Ω respectively. The voltage across the load lies between :

• 11.7 V and 11.8 V

• 11.6 V and 11.7 V

• 11.5 V and 11.6 V

• 11.4 V and 11.5 V

In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t

$i = 20 \sin \left(30 t -\frac{\pi }{4}\right)$

In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively

• 50,0

• 50,10

• $\frac{1000}{\sqrt{2}}, 10$

• $\frac{50}{\sqrt{2}},0$

An EM wave from air enters a medium. The electric fields are

${\overrightarrow{E}}_1 = E_{01} \hat{x} \cos \left[2\pi v\left(\frac{z}{c}-t\right)\right]$ in air and ${\overrightarrow{E}}_2 = E_{02} \hat{x} \cos [ k(2z-ct\left)\right]$ in medium, where the wave number k and frequency v refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r_1} and {\epsilon }_{r_2}$refer to relative permittivities of air and medium respectively, which of the following options is correct ?

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = \frac{1}{2}$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = 4$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = 2$

• $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}} = \frac{1}{4}$