1.

STATEMENT – 1
Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
STATEMENT – 2
Principle of conservation of momentum holds true for all kinds of collisions.

• The statement I is True, Statement II is False.

• The statement I is True, Statement II is True; Statement II is a correct explanation for Statement I.

• The statement I is True, Statement II is True; Statement II is not the correct explanation for Statement I.

• The statement I is True, Statement II is True; Statement II is not the correct explanation for Statement I.

A particle is moving with velocity, where K is a constant. The general equation for its path is

• y = x² + constant

• y² =  x + constant

• xy = constant

• xy = constant

The figure shows the position –time (x – t) graph of one–dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

• 0.4 (Ns)

• 0.8 Ns

• 1.6 Ns

• 1.6 Ns

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10^–3 are

• 5,1,2

• 5,1,5

• 5,5,2

• 5,5,2

A point p moves in counter -clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out the length s = t3 + 5, where s is metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2 s is nearly

• 13 ms^-2

• 12 ms^-2

• 7.2 ms^-2

• 7.2 ms^-2

Two fixed frictionless inclined planes making an angle 30° and 60° with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

• 4.9 ms^-2 in horizontal direction

• 9.8 ms^-2 in vertical direction

• zero

• zero

For a particle in uniform circular motion, the acceleration an at point P (R, θ) on the circle of radius R is (Here θ is measured from the x–axis)

A small particle of mass m is projected at an angle θ with the x–axis with an initial velocity v₀ in the x–y plane as shown in the figure. At a time t<v_osin/g, the angular momentum of the particle is

A ball is made of a material of density ρ where ρ_oil < ρ < ρ_water with ρ_oil and ρ_water representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V,the efficiency of the engine is

• 0.5

• 0.75

• 0.99

• 0.99