Motion in A Plane

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

• its velocity is constant

• its acceleration is constant

• its kinetic energy is constant

• its kinetic energy is constant

Two masses m₁ = 5 kg and m₂ = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of the horizontal surface is 0.15. The minimum weight m that should be put on top of m₂ to stop the motion is :

• 10.3 kg

• 18.3 kg

• 27.3 kg

• 43.3 kg

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is:

• 

• v_o/4

• 

• v₀/2

From the ground, a projectile is fired at an angle of 60 degrees to the horizontal with a speed of 20 m/s. Take, acceleration due to gravity as 10 m/s² . The horizontal range of the projectile is

• $10\sqrt{3} \mathrm{m}$

• 20 m

• $20\sqrt{3}$

• $40\sqrt{3} \mathrm{m}$

A ball falls from a table top with initial horizontal speed V₀. In the absence of air resistance,which of the following statement is correct.

• The vertical component of the acceleration changes with time

• The horizontal component of the velocity does not change with time

• The horizontal component to the acceleration is non zero and finite

• The time taken by the ball to touch the ground depends on V₀

A man of mass 60 kg climbed down using an elevator.The elevator had an acceleration 4 ms^-2. If the acceleration due to gravity is 10 ms^-2, the man's apparent weight on his way down is

• 60 N

• 240 N

• 360 N

• 840 N

A uniform rod of length of 1 m arid mass of 2 kg is attached to a side support at O as shown in the figure. The rod is at equilibrium due to upward force T acting at P. Assume the acceleration due to gravity as 10 m/s² . The value of T is

• 0

• 2 N

• 5 N

• 10 N

An aeroplane is flying with a uniform speed of 150 km h^-1 along the circumference of a circle. The change in its velocity in half the revolution (in km h^-1) is

• 150

• 100

• 200

• 300

In uniform circular motion, the centripetal acceleration is

• towards the centre of the circular path and perpendicular to the instantaneous velocity

• a constant acceleration

• away from the centre of the circular path and perpendicular to the instantaneous velocity

• a variable acceleration making 45° with the instantaneous velocity

A body is thrown up with a speed u, at an angle of projection θ. If the speed of the projectile becomes $\frac{\mathrm{u}}{\sqrt{2}}$on reaching the maximum height, then the maximum vertical height attained by the projectile is

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

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

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

• $\frac{{\mathrm{u}}^2}{\mathrm{g}}$