Two particles of mass m₁ and m₂ approach each other due to their mutual gravitational attraction only. Then

• accelerations of both the particles are equal

• acceleration of the particle of mass m₁ is proportional to m₁

• acceleration of the particle of mass m₁ is proportional to m₂

• acceleration of the particle of mass m₁ is inversely proportional to m₁

A satellite has kinetic energy K, potential energy V and total energy E. Which of the following statements is true ?

• K = − V/2

• K = V/2

• E = K/2

• E = − K/2

A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the centre of mass of the system from the origin is

• equal to R

• less than equal to R

• greater than R

• greater than equal to R

Two particles A and B are moving as shown in the figure.

Their total angular momentum about the point O is

• 9.8 kg m² / s

• zero

• 52.7 kg m² / s

• 37.9 kg m² / s

Particle A moves along X-axis with a uniform velocity of magnitude 10 m/s. Particle B moves with uniform velocity 20 m/s along a direction making an angle of 60° with the positive direction of X-axis as shown in the figure. The relative velocity of B with respect to that of A is

• 10 m/s along X-axis

• $10\sqrt{3}$ m/s along Y-axis (perpendicular to X-axis)

• $10\sqrt{5}$ m/s along the bisection of the velocities of A and B

• 30 m/s along negative X-axis

Block B lying on a table weighs W. The coefficient of static friction between the block and the table is µ. Assume that the cord between B and the knot is horizontal. The maximum weight of the block A for which the system will be stationary is

• $\frac{\mathrm{W} \tan \mathrm{\theta }}{\mathrm{\mu }}$

• µW tan θ

•  $\mathrm{\mu W} \sqrt{1 + {\tan }^2 \mathrm{\theta }}$

• µW sin θ

Two particles A and B having different masses are projected from a tower with same speed. A is projected vertically upward and B vertically downward. On reaching the ground

• velocity of A is greater than that of B

• velocity of B is greater than that of A

• both A and B attain the same velocity

• the particle with the larger mass attains higher velocity

A cylinder of height h is filled with water and is kept on a block of height h/2. The level of water in the cylinder is kept constant. Four holes numbered 1,2, 3 and 4 are at the side of the cylinder and at heights 0, h/4, h/2 and 3h/4, respectively. When all four holes are opened together, the hole from which water will reach farthest distance on the plane PQ is the hole number

• 1

• 2

• 3

• 4

A circular disc rolls on a horizontal floor without slipping and the centre of the disc moves with a uniform velocity v. Which of the following values of the velocity at a point on the rim of the disc can have ? 

• v

• − v

• 2v

• Zero

Three bodies of the same material and having masses m, m and 3m are at temperatures 40°C, 50° C and 60° C, respectively. If the bodies are brought in thermal contact, the final temperature will be

• 45°C

• 54°C

• 52°C

• 48°C