$A$ car travelling on a smooth road passes through a curved portion of the road in the form of an arc of a circle of radius $10 \, m$. If the mass of the car is $500 \, kg$,the reaction on the car at the lowest point $P$ where its speed is $20 \, m/s$ is ......... $kN$.

$A$ $500\, kg$ crane takes a turn of radius $50\, m$ with a velocity of $36\, km/hr$. The centripetal force is ......... $N$.

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is :
$(i) \; T$
$(ii) \; T - \frac{m v^{2}}{l}$
$(iii) \; T + \frac{m v^{2}}{l}$
$(iv) \; 0$
$T$ is the tension in the string. [Choose the correct alternative].

$A$ body of mass $10 \,g$ is tied to a string of length $0.4 \,m$ and it is whirled in a horizontal plane with a speed of $6 \,m/s$. Then the tension in the string is (in $\,N$)

$A$ string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $(\frac{3}{\pi})$ rotations per second about the vertical axis passing through the fixed end of the string as shown. The tension in the string is . . . . . . $ML$.

"Momentum and changes in momentum are not always in the same direction." Explain with a suitable example.