Laws of Motion

An ice cart of mass 60 kg rests on a horizontal snow patch with coefficient of static friction $\frac{1}{3}$. Assuming that there is no vertical acceleration, find the magnitude of the maximum horizontal force required to move the ice cart. (g= 9.8 ms^-2)

• 100 N

• 110 N

• 209 N

• 196 N

A cyclist is moving in a circular track of radius 80 m with a velocity v = 36 km/h. He has to lean from the vertical approximately through an angle (Take g = 10 ms^-2)

• ${\tan }^{-1} \left(4\right)$

• ${\tan }^{-1} \left(\frac{1}{3}\right)$

• ${\tan }^{-1} \left(\frac{1}{4}\right)$

• ${\tan }^{-1} \left(\frac{1}{8}\right)$

An athlete throws a discus from rest to a final angular velocity of 15 rad/s in 0.270 s before releasing it. During acceleration, discus moves a circular arc of radius 0.810 m. Acceleration of discus before it is released is

• 45

• 182

• 187

• 192

From the top of tower, a stone is thrown up. It reaches the ground in t₁ second. A second stone thrown down with the same speed reaches theground in t₂ second. A third stone released from rest reaches the ground in t₃ second. Then

• ${\mathrm{t}}_{3 }= \frac{\left({\mathrm{t}}_1 + {\mathrm{t}}_2\right)}{2}$

• ${\mathrm{t}}_3 = \sqrt{{\mathrm{t}}_1 + {\mathrm{t}}_2}$

• $\frac{1}{{\mathrm{t}}_3} = \frac{1}{{\mathrm{t}}_1} - \frac{1}{{\mathrm{t}}_2}$

• ${\mathrm{t}}_3^2 = {\mathrm{t}}_{2 }^2- {\mathrm{t}}_1^2$

A player caught a cricket ball of mass 150 g moving at the rate of 20 ms^-1 . If the catching process be completed in 0.1 s, the force of the blow exerted by the ball on the hands of the player is

• 0.3 N

• 30 N

• 300 N

• 3000 N

A uniform metal chain is placed on a rough table such that one end of it hangs down over the edge of the table.  When one-third of its length hangs over the edge, the chain starts sliding. Then, the coefficient of static friction is

• $\frac{3}{4}$

• $\frac{1}{4}$

• $\frac{2}{3}$

• $\frac{1}{2}$

Two masses M and M/2 are joined together by means of light inextensible string passed over a frictionless pulley as shown in the figure. When the bigger mass is released, the small one will ascend with an acceleration of

• $\frac{\mathrm{g}}{3}$

• $\frac{3\mathrm{g}}{2}$

• $\frac{\mathrm{g}}{2}$

• g

A boy of mass 40 kg is climbing a vertical pole at a constant speed. If the coefficient of friction between his palms and the pole is 0.8 and g = 10 m/s², the horizontal force that he is applying on the pole is

• 300 N

• 400 N

• 500 N

• 600 N

A cricket ball of mass 0.25 kg with speed 10 m/s collides with a bat and returns with same speed within 0.01 s. The force acted on bat is

• 25 N

• 50 N

• 250 N

• 500 N

If the earth were to suddenly contract to $\frac{1}{\mathrm{n}}\mathrm{th}$ of its present radius without any change in its mass, the duration of the new day will be nearly

• 24/n h

• 24 n h

• 24/n² h

• 24 n² h