Two solds P and Q float in water. It is observed that P floats with half of its volume immersed and Q floats with $\frac{2}{3}$rd of its volume is immersed. The ratio of densities of P and Q is

• $\frac{4}{3}$

• $\frac{3}{4}$

• $\frac{2}{3}$

• $\frac{3}{2}$

The equation of a transverse wave is given by $\mathrm{y} = 0.05 \sin \mathrm{\pi } \left(2\mathrm{t} - 0.02 \mathrm{x}\right)$, where x, y are in metre and t is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively

• 50 m, 50 ms^-1

• 100 m, 100 ms^-1

• 50 m, 100 ms^-1

• 100 m, 50 ms^-1

The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is

• 2 : 1

• 1 : 2

• 1 : 3

• 3 : 1

A person with vibrating tuning fork of frequency 338 Hz is moving towards a vertical wall with a speed of 2 ms^-1 . Velocity of sound in air is 340 ms^-1. The number of beats heard by that person per second is

• 2

• 4

• 6

• 8

15.

A small oil drop ofmass 10^-6 kg is hanging in at rest between two plates separated by 1 mm having a potential difference of 500 V. The charge on the drop is (g = 10 ms^-2)

• 2 × 10^-9 C

• 2 × 10^-11 C

• 2 × 10^-6 C

• 2 × 10^-9 C

A uniform electric field in the plane of the paper as shown. Here A, B, C and D are the ponits on the circle. V₁, V₂, V₃ and V₄ are the potentials at those points respectively. Then

• V_A = V_C, V_B = V_D

• V_A = V_C, V_B > V_D

• V_A > V_C, V_B > V_D

• V_A = V_B, V_C > V_D

Two metal spheres of radii 0.01 m and 0.02 m are given a charge of 15 mC and 45 mC respectively. They are then connected by a wire. The final charge on the first sphere is

• 40 × 10^-3 C

• 30 × 10^-3 C

• 20 × 10^-3 C

• 10 × 10^-3 C

The concentric spheres of radii R and r have positive charges q₁ and q₂ with equal surface charge densities. What is the electric potential at their common centre ?

• $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0} \left(\mathrm{R} + \mathrm{r}\right)$

• $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0} \left(\mathrm{R} - \mathrm{r}\right)$

• $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0} \left(\frac{1}{\mathrm{R}} + \frac{1}{\mathrm{r}}\right)$

• $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0} \left(\frac{1}{\mathrm{R}}\right)$

When an additional charge of 2C is given to a capacitor, energy stored in it is increased by 21%. The original charge of the capacitor is

• 30 C

• 40 C

• 10 C

• 20 C

When a potential difference of 10³ V is applied between A and B, a charge of 0. 75 mC is value of C is (in μF)

• $\frac{1}{2}$

• 2

• 2.5

• 3