Laws of Motion

A body takes time t to reach the bottom of an inclined plane of angle 0 with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is:

• $\frac{3}{4}\mathrm{tan\theta }$

• $\frac{2}{3}\mathrm{tan\theta }$

• $\frac{1}{4}\mathrm{tan\theta }$

• $\frac{1}{2}\mathrm{tan\theta }$

Two bodies having masses m₁ = 40g and m₂ = 60 g are attached to the ends of a string of negligible mass and suspended from a massless pulley. The acceleration of the bodies is:

• 1 m/s²

• 2 m/s²

• 0.4 m/s²

• 4 m/s²

A block is moving up an inclined plane of inclination 60° with a velocity of 20 m/s and stops after 2 s. If g = 20 m/s² then the approximate value of the coefficient of friction is :

• 3

• 3.3

• 0.27

• 0.33

A force of 49 newtons is just able to move a block of wood weighing 10 kg-on a rough horizontal surface. Its coefficient of friction is :

• 1

• 0.7

• 0.5

• zero

Two bodies of mass m and 4m have equal kinetic energy. What is the ratio of their momentum?

• 1 : 4

• 1 : 2

• 1 : 1

• 2 : 1

A particle is moving in a circle with uniform speed v. In moving from a point to another diametrically opposite point :

• the momentum changes by mv

• the momentum changes by 2mv

• the kinetic energy changes by 1/2 mv²

• the kinetic energy changes by mv²

A block of mass 1 kg is placed on the wall under a force F. If coefficient of friction ($\mathrm{\mu }$) is 0.5, then minimum value of force applied is :

• 9.8 N

• 49 N

• 19.6 N

• 1.96 N

A car is moving with speed 30 m/s on a circular path of radius 500 m. If its speed is increasing at a rate of 5m/s², then resultant acceleration at that instant is

• 6.83 m/s²

• 8 m/s²

• 5.31 m/s²

• 4 m/s²

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/s. The tension in the string is 6 N, when the stone is a

• top of the circle

• bottom of the circle

• halfway down

• None of the above

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