Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is

• (i) – 10 J (ii) –8.25 J

• (i) 1.25 J (ii) –8.25 J

• (i) 100 J (ii) 8.75 J

• (i) 100 J (ii) 8.75 J

12.

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of the disc with angular velocities ω₁ and ω₂. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

• 
• 
• 
• 

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk up on the moving escalator will be

A gas mixture consists of 2 moles of O₂ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

• 4 RT

• 15 RT

• 9 RT

• 9 RT

A U tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile, the water rises by 65 mm from its original level (see diagram). The density of the oil is

• 650 kg m^–3

• 425 kg m^–3

• 800 kg m^–3

• 800 kg m^–3

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is

Two rods A and B of different materials are welded together as shown in the figure. Their thermal conductivities are K₁ and K₂. The thermal conductivity of the composite rod will be

• 
• 

• k₁ + k₂

• k₁ + k₂

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

Thermodynamic processes are indicated in the following diagram.

Match the following

• P → a, Q → c, R → d, S → b

• P → c, Q → a, R → d, S → b

• P → c, Q → d, R → b, S → a

• P → c, Q → d, R → b, S → a

A spring of force constant k is cut into lengths of ratio 1: 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is

• 1:6

• 1:9

• 1:11

• 1:11