Three point charges 1 C, 2C and 3C are placed at the corners of an equilateral triangle of side 1 m. The work done in bringing these charges to the vertices of a smaller similar triangle of side 0.5 m is

• 2.7 × 10¹⁰ J

• 9.9 × 10¹⁰ J

• 10.8 × 10¹⁰ J

• 5.4 × 10¹⁰ J

In a simple pendulum the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle θ with the vertical. Then

• θ = 30°

• θ = 45°

• θ = cos^-1 (2/3)

• θ = cos^-1 (1/3)

An object of mass m falls on to a spring of constant k from h. Then the spring undergoes compression by a length a. The maximum compression x is given by the equation

• $\mathrm{mgh} = \frac{1}{2} {\mathrm{kx}}^2$

• $\mathrm{mg} \left(\mathrm{h} + \mathrm{x}\right) = \frac{1}{2} {\mathrm{kx}}^2$

• $\mathrm{mg} \left(\mathrm{h} + \mathrm{x}\right) = - \mathrm{kx}$

• mgh = − kx

An adulterated sample of milk has a density of 1032 kgm^-3, while pure milk has a density of 1080 kgm^-3. Then the volume of pure milk in a sample of 10 L of adulterated milk is

• 0.5 L

• 1.0 L

• 4.0 L

• 3.0 L

Typical silt (hard mud) particle of radius 20 µm is on the top of lake water, its density is 2000 kg/m³  and the viscosity of lake water is 1.0 mPa, density is 1000 kg/m³. If the lake is still (hos no internal fluid motion). The terminal speed with which the particle hits the bottom of the lake is 

• 0.67 mm/s

• 0.77 mm/s

• 0.87 mm/s

• 0.97 mm/s

If P is the pressure, V the volume, R the gas constant, k the Boltzmann constant and T the absolute temperature, then the number of molecules in the given mass of the gas is given by

• $\frac{\mathrm{PV}}{\mathrm{RT}}$

• $\frac{\mathrm{PV}}{\mathrm{kT}}$

• $\frac{\mathrm{PR}}{\mathrm{T}}$

• pV

27.

An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is 100 kPa, the absolute pressure at the bottom of lake in kPa is (assume no temperature variation):

• 33.3

• 50.0

• 300.0

• 200.0

During an adiabatic process, the volume of a gas is found to be proportional to the cube of its absolute temperature. The ratio C_p / C_V for the gas is

• 5/3

• 4/3

• 3/2

• 5/4

1 g of steam at 100°C and equal mass of ice at 0°C are mixed. The temperature of the mixture in steady state will be (latent heat of steam = 540 cal/g, latent heat of ice = 80 cal/g)

• 50°C

• 100°C

• 67°C

• 33°C

The work done by a gas is maximum when it expands

• isothermally

• adiabatically

• isentropically

• isobarically