If a closed organ pipe of length L₁ in its fundamental mode resonates with an open organ pipe of length L₂ then L₁ : L₂ is

• 1 : 2

• 2 : 1

• 1 : 4

• 4 : 1

The physical quantity that remains unchanged when a sound wave goes from one medium to another is

• amplitude

• speed

• wavelength

• frequency

The beat frequency observed when two sound waves y₁ = 0.5 sin (410 t) and y₂ = 0.5 sin ( 454 t) travel in the same direction is

• 5

• 3

• 7

• 2

A magnet takes a minute to make 30 oscillations in a magnetic field. If the field strength is doubled, then the time period of oscillation (in sec) is

• $\sqrt{2}$

• $2\sqrt{2}$

• $\frac{\sqrt{3}}{2}$

• $\sqrt{3}$

If the time period of oscillation of a pendulum is measured as 2.5 s using a stop watch with the leas tcount $\frac{1}{2}$s, then the permissible error in the measurement is

• 10 %

• 30 %

• 20 %

• 25 %

Two identical thin rings, each of radius 10 cm carrying charges 10 C and 5 C are coaxially placed at a distance 10 cm apart. The work done in moving a charge q from the centre of the first ring to that of the second is

• $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle +}{\displaystyle }{\displaystyle 1}}{\sqrt{2}}\right)$

• $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle -}{\displaystyle 1}{\displaystyle }}{\sqrt{2}}\right)$

• $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle +}{\displaystyle }{\displaystyle 1}}{\sqrt{2}}\right)$

• $\frac{\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0} \left(\frac{\sqrt{2}{\displaystyle }{\displaystyle -}{\displaystyle }{\displaystyle 1}}{\sqrt{2}}\right)$

37.

The electric potential V at any point (x, y, z) in space is given by V = 3x² where x, y, z are all in metre. The electric field at the point (1 m, 0, 2 m) is

• 6 V m^-1  along negative x-axis 

• 6 V m^-1  along positive x-axis 

• 12 V m^-1  along negative x-axis 

• 12 V m^-1 along positive x-axis 

Choose the correct statement

• Polar molecules have permanent electric dipole moment

• CO₂  molecule is a polar molecule 

• H₂O  is a non-polar molecule

• The dipole field at large distances falls of as $\frac{1}{{\mathrm{r}}^2}$

The electric field between two infinitely charged plates with air medium in between, in terms of the surface charge density σ is

• $4{\mathrm{\pi \epsilon }}_0$

• $\frac{\mathrm{\sigma }}{4{\mathrm{\pi \epsilon }}_0}$

• $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}$

• $\frac{4\mathrm{\pi \sigma }}{{\mathrm{\epsilon }}_0}$

Two equal point charges each of 3 µC are separated by a certain distance in metres. If they are located at (i + j + k)and (2i + 3j + k), then the electrostatic force between them is

• 9 × 10³ N

• 9 × 10^-3 N

• 16.5 × 10^-3 N

• 3 × 10^-3 N