A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity $\sqrt{3\mathrm{gr}}$ at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

• 4 : 3

• 5 : 4

• 1 : 4

• 3 : 2

The potential energy of a conservative system is given by V(x) = (x² − 3x) joule, where x is measured in metre. Then its equilibrium position is at

• 1.5 m

• 2 m

• 3 m

• 1 m

Two bodies of masses 4 kg and 9 kg are separated by distance of 60 cm. A 1 kg mass is placed in between these two masses. If the net force on 1 kg is zero, then its distance from 4 kg mass is

• 26 cm

• 30 cm

• 24 cm

• 32 cm

Two spherical rain drops with radii in the ratio 1 : 2 fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is

• 1 : 8

• 2 : 1

• 1 : 32

• 1 : 2

The sum of magnitudes of two forces acting at a point is 16 N and their resultant $8\sqrt{3}$ N is at 90° with the force of smaller magnitude. The two forces (in N) are

• 11, 5

• 9, 7

• 2, 14

• 4, 12

Among the following, the vector quantity is

• pressure

• gravitation potential

• stress

• impulse

A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force $\mathrm{F} = \frac{\mathrm{k}}{{\mathrm{r}}^2}$, where k is a constant.

• The potential energy of the particle is zero

• The potential energy of the particle is $\frac{\mathrm{k}}{\mathrm{r}}$

• The total energy of the particle is $-\frac{\mathrm{k}}{2\mathrm{r}}$

• The kinetic energy of the particle is $- \frac{\mathrm{k}}{\mathrm{r}}$

A passenger getting down from a moving bus, falls in the direction of the motion of the bus. This is an example for

• moment of inertia

• second law of motion

• inertia of motion

• inertia of rest

A body of mass 6 kg is hanging from another body of mass 10 kg as shown in figure. This combination is being pulled up by a string with an acceleration of 2 ms^-2. The tension T₁ is, (g =10 ms^-2)

• 240 N

• 150 N

• 220 N

• 192 N

Which one of the following is not a contact force ?

• Viscous force

• Air resistance

• Magnetic force

• Buoyant force