Laws of Motion

The minimum velocity (in ms^-1) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction to avoid skidding is

• 60

• 30

• 15

• 25

A body of mass 3 kg is acted on by a force which varies as shown in the graph. The momentum acquired is given by

• zero

• 5 N-s

• 30 N-s

• 50 N-s

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

• $\sqrt{2} \mathrm{Mg}$

• $\sqrt{2} \mathrm{mg}$

• $\sqrt{{\left(\mathrm{M}\hspace{0.17em}+ \mathrm{m}\right)}^2 + {\mathrm{m}}^2\mathrm{g}}$

• $\sqrt{{\left(\mathrm{M} + \mathrm{m}\right)}^2 + {\mathrm{M}}^2} \mathrm{g}$

A body of mass 5 kg moves on a straight path as a function of time x = t³ − 12t. The force on the body at t = 5s will be

• 100 N

• 150 N

• 120 N

• 130 N

n balls each of mass m impinge elastically each second on a surface with velocity v. The average force experienced by the surface will be

• 2nmv

• nmv

• $\frac{\mathrm{nmv}}{2}$

• 4nmv

The angle to which a cyclist bends when he covers a circular path of 34.3 m in $\sqrt{22}$ s is

• 20°

• 30°

• 60°

• 45°

A gun of mass M fires a bullet of mass m with velocity v. Then, the recoil speed of the gun will be

• $-\frac{\mathrm{m}}{\mathrm{M}}\mathrm{v}$

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

• $\frac{\mathrm{M}}{\mathrm{m}}\mathrm{v}$

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

If the coefficient of static friction between the tyres and road is 0.5, what is the shortest distance in which an automobile can be stopped when travelling at 72 kmh^-1 ?

• 50 m

• 60 m

• 40.8 m

• 80.16 m

The upper half of an inclined plane with inclination $\mathrm{\varphi }$ is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by

• 2 sin $\mathrm{\varphi }$

• 2 cos $\mathrm{\varphi }$

• 2 tan $\mathrm{\varphi }$

• tan $\mathrm{\varphi }$

Two blocks of masses 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30° with the horizontal whereas 5 kg block hangs freely. The tension (T) in the string is

• 48.56 N

• 72.22 N

• 32.56 N

• 24.65 N