In a uniform circular motion, the angle between the velocity and acceleration is

• 0

• 45°

• 90°

• 75°

In the entire path of a projectile, the quantity that remains unchanged is

• vertical component of velocity

• horizontal component of velocity

• kinetic energy

• potential energy

A block of mass 10 kg is moving horizontally with a speed of 1.5 ms^-1 on a smooth plane. If a constant vertical force 10 N acts on it, the displacement of the block from the point of application of the force at the end of 4 s is

• 5 m

• 20 m

• 12 m

• 10 m

A block of weight 4 kg is resting on a smooth horizontal plane. If it is struck by a jet of water at the rate of 2 kgs^-1 and at the speed of 10 ms^-1, then the initial acceleration of the block is

• 15 ms^-2

• 10 ms^-2

• 5 ms^-2

• 1 ms^-2

Two projectiles A and B thrown with speeds in the ratio 1 : $\sqrt{2}$ acquired the same heights. If A is thrown at an angle of 45° with the horizontal, the angle of projection of B will be

• 0°6

• 60°

• 30°

• 45°

A block at rest slides down a smooth inclined plane which makes an angle 60° with the vertical and it reaches the ground in t₁ seconds. Another block is dropped vertically from the same point and reaches the ground in t₂ seconds. Then the ratio of t₁ : t₂ is

• 1 : 2

• 2 : 1

• 1 : 3

• $1 : \sqrt{2}$

57.

A ball of mass m is dropped from a height h on a platform fixed at the top of a vertical spring, as shown in figure. The platform is depressed by a distance x. Then the spring constant is

• $\frac{\mathrm{mg}}{\left(\mathrm{h} + \mathrm{x}\right)}$

• $\frac{\mathrm{mg}}{\left(\mathrm{h} + 2\mathrm{x}\right)}$

• $\frac{2\mathrm{mg} \left(\mathrm{h} + \mathrm{x}\right)}{{\mathrm{x}}^2}$

• $\frac{\mathrm{mg}}{\left(2\mathrm{h} + \mathrm{x}\right)}$

A ring starts to roll down the inclined plane of height h without slipping. The velocity with which it reaches the ground is

• $\sqrt{\frac{1\mathrm{Ugh}}{7}}$

• $\sqrt{\frac{4\mathrm{gh}}{7}}$

• $\sqrt{\mathrm{gh}}$

• $\sqrt{2\mathrm{gh}}$

The angular momentum of a particle describing uniform circular motion is L. If its kinetic energy is halved and angular velocity doubled, its new angular momentum is

• 4 L

• $\frac{\mathrm{L}}{4}$

• $\frac{\mathrm{L}}{2}$

• 2 L

The maximum height of a projectile is half of its range on the- horizontal. If the velocity of projection is u, its range on the horizontal is

• $\frac{2{\mathrm{u}}^2}{5\mathrm{g}}$

• $\frac{3{\mathrm{u}}^2}{5\mathrm{g}}$

• $\frac{4{\mathrm{u}}^2}{5\mathrm{g}}$

• $\frac{{\mathrm{u}}^2}{5\mathrm{g}}$