The potential energy of particle varies with distance x fixed a origin as $v = \left(\frac{A\sqrt{x}}{x + B}\right)$; where A and B are constants. The dimensions of AB are

• [ M L^5/2 T^-2 ]

• [ M L² T^-2 ]

• [ M^3/2 L^3/2 T^-2 ]

• [M L^7/2 T^-2 ]

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 min a vertical plane. If g = 10 ms^-2,  then the maximum angular velocity the stone will be

• 2 rad s^-1

• 4 rad s^-1

• 8 rad s^-1

• 16 rad s^-1

Two spherical bodies of masses M and SM and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision,

• 1.5 R

• 2.5 R

• 4.5 R

• 7.5 R

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

• MR²

• $\frac{1}{2} {\mathrm{MR}}^2$

• $\frac{3}{2} {\mathrm{MR}}^2$

• $\frac{7}{2} {\mathrm{MR}}^2$

A satellite orbiting the earth in a circular orbit of radius R completes one revolution in 3h. If orbital radius of geostationary satellite is 36000 km, orbital radius of earth is

• 6000 km

• 9000 km

• 12000 km

• 15000 km

A wire can be broken by applying load of 200 N. The force required to break another wire of the same length and same material, but double in diameter is

• 200 N

• 400 N

• 600 N

• 800 N

A cube of side 40 mm has its upper face displaced by 0.1 mm by a tangential force of 8 kN. The shearing modulus of cube is

• 2 × 10⁹ Nm^-2

• 4 × 10⁹ Nm^-2 

• 8 × 10⁹ Nm^-2

• 16 × 10⁹ Nm^-2

The neck and bottom of a bottle are 3 cm and 15 cm in radius respectively. If the cork is pressed with a force 12 N in the neck of the bottle, then force exerted on the bottom of the bottle is

• 30 N

• 150 N

• 300 N

• 600 N

A square wire frame of size L is dipped in a liquid. On taking out a membrane is formed. If the surface tension of liquid is T, then force acting on a frame will be

• 2T L

• 4T L

• 8T L

• 16T L

10.

64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms^-1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

• 8 ms^-1

• 16 ms^-1

• 24 ms^-1

• 32 ms^-1