Two chambers containing m₁ g and m₂ g of a gas at pressures P₁ and P₂ respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

• $\frac{{\mathrm{P}}_1{\mathrm{P}}_2 \left( {\mathrm{m}}_1 + {\mathrm{m}}_2 \right)}{\left( {\mathrm{P}}_2 {\mathrm{m}}_1 + {\mathrm{P}}_1 {\mathrm{m}}_2 \right)}$

• $\frac{{\mathrm{P}}_1 {\mathrm{P}}_2 {\mathrm{m}}_1}{{\mathrm{P}}_2{\mathrm{m}}_1 + {\mathrm{P}}_1 {\mathrm{m}}_2}$

• $\frac{{\mathrm{m}}_1 {\mathrm{m}}_2 \left({\mathrm{P}}_1 + {\mathrm{P}}_2\right)}{{\mathrm{P}}_2 {\mathrm{m}}_1 + {\mathrm{P}}_1{\mathrm{m}}_2}$

• $\frac{{\mathrm{m}}_1 {\mathrm{m}}_2{\mathrm{P}}_2}{{\mathrm{P}}_2 {\mathrm{m}}_1 + {\mathrm{P}}_1{\mathrm{m}}_2 }$

22.

A particle is describing simple harmonic motion. If its velocities are v₁ and v₂ when the displacements from the mean position are y₁ and y₂ respectively, then its time period is

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{y}}_1^2 + {\mathrm{y}}_2^2}{{\mathrm{v}}_1^2 + {\mathrm{v}}_2^2}}$

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{v}}_2^2 - {\mathrm{v}}_1^2}{{\mathrm{y}}_1^2 - {\mathrm{y}}_2^2}}$

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{v}}_1^2 + {\mathrm{v}}_2^2}{{\mathrm{y}}_1^2 + {\mathrm{y}}_2^2}}$

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{y}}_1^2 - {\mathrm{y}}_2^2}{{\mathrm{v}}_2^2 - {\mathrm{v}}_1^2}}$

When an ideal monoatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

• 2 / 5

• 3 / 5

• 3 / 7

• 5 / 7

When a stretched wire and a tuning fork are sounded together, 5  beats per second are produced, when length of wire is  95 cm or 100 cm, frequency of the fork is

• 90 Hz

• 100 Hz

• 105 Hz

• 195 Hz

Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane as shown in the figure. If the mass M is displaced in the horizontal direction, then the frequency of the system is

A Carnot engine operates with source at 127°C and sink at 27°C. If the source supplies 40 kJ of heat energy, the work done by the engine is

• 30 kJ

• 10 kJ

• 4 kJ

• 1 kJ

Assertion:  A rigid body can be elastic.

Reason: If s force is applied on the rigid, its dimensions may change.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion: A piece of ice, with a stone frozen inside it, floats on water in a beaker. When the ice melts, the level of water in the beaker decreases.

Reason:  Density ofstone is more than that of water.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  A particle in x-y plane is related by   x = $\mathrm{\alpha }$ sin t and  y =  $\mathrm{\alpha }$ (l - cos t), where $\mathrm{\alpha }$ and ω are constants, then the particle will have parabolic motion.

Reason:  A particle under the influence of two perpendicular velocities has parabolic motion.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  A needle placed carefully on the surface of water may float, whereas the ball of the same material will always sink. 

Reason:  The buoyancy of an object depends both on the materials and shape of the object.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.