If a body travels half the distance with velocity v₁ and the next half with velocity v₂,its average velocity will be given by

• $\mathrm{v} = \sqrt{{\mathrm{v}}_1{\mathrm{v}}_2}$

• $\mathrm{v} = \frac{{\mathrm{v}}_1 + {\mathrm{v}}_1}{2}$

• $\mathrm{v} = \frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$

• $\frac{2}{\mathrm{v}} = \frac{1}{{\mathrm{v}}_1} + \frac{1}{{\mathrm{v}}_2}$

The ratio of the numerical value of the average velocity and average speed of body is always

• unity

• unity or less

• unity or more

• less than unity

Mark the correct option.
If a ball is projected with velocity v₀ at an angle of elevation 30°, then

• gravitational potential energy will, be minimum at the highest point of the trajectory

• kinetic energy will be zero at the highest point of the trajectory

• vertical component of momentum will be conserved

• horizontal component of momentum will be conserved

A spring scale is adjusted to read zero. Particles of mass 1 g fall on the pan of the scale and collide elastically and they rebound upward with the same speed. If the height of fall of particles is 2 m and their rate of collision is 100 particles per second, then the scale reading in grams will be (g =9.8 m/s)?

• 1000 g

• 1100 g

• 1200 g

• 1252 g

A smooth sphere of mass m moving with velocity u directly collides elastically with another sphere of mass M at rest. After collision their final velocities are V and v respectively. The value of v is

• $2\mathrm{u} \frac{\mathrm{M}}{\mathrm{m}}$

• $2\mathrm{u} \frac{\mathrm{m}}{\mathrm{M}}$

• $\frac{2 \mathrm{u}}{1 + {\displaystyle \frac{\mathrm{m}}{\mathrm{M}}}}$

• $\frac{2 \mathrm{u}}{1 + {\displaystyle \frac{\mathrm{M}}{\mathrm{m}}}}$

A block of mass 2 kg is kept on the floor. The coefficient of static friction is 0.4. If a force F of 2.5 N is applied on the block as shown in the figure, the frictional force between the block and the floor will be

• 2.5 N

• 5 N

• 7.84 N

• 10 N

The moments of inertia of two freely rotating bodies A and B are I_A and I_B respectively I_A > I_B and their angular momenta are equal. If K_A and K_B are their kinetic energies then

• K_A = K_B

• K_A > K_B

• K_A < K_B

• K_A = 2 K_B

A wheel of car is revolving at the rate of 1200 cycle/min. On pressing the accelerator, after 10s, it does 4500 cycle/min then radial acceleration of the wheel is

• 30 rad/s²

• 1880 degree/s²

• 40 rad/s²

• 1980 degree/s²

If the height of a satellite from the earth is negligible in comparison to the radius of the earth R, the orbital velocity of the satellite is

• gR

• $\frac{\mathrm{gR}}{2}$

• $\sqrt{\frac{\mathrm{g}}{\mathrm{R}}}$

• $\sqrt{\mathrm{gR}}$

A satellite is revolving round the earth in an elliptical orbit. Its speed

• will be same at all points of the orbit

• will be maximum when it is at maximum distance from earth

• will be maximum when its distance from the earth will be minimum

• goes on increasing or decreasing continuous depending upon the mass of the satellite