A body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimetre. If the angular velocity is doubled, the elongation in the spring is $5\, cm$ . The original length of the spring is ............ $cm$

A motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between road and tyres is $0.5$, the speed avoiding skidding will be ....... $m/s$

A motor car has a width $1.1$ m between wheels. Its centre of gravity is $0.62$ m above the ground and the coefficient of friction between the wheels and the road is $0.8$. ...... $m/s$  is the maximum possible speed, if the centre of gravity inscribes a circle of radius $15$ m ? (Road surface is horizontal)

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$. Which of the following curve represents the correct relation between the normal reaction on the block by the wall $( N )$ and speed of the block $(v)$ ?

A block of mass $10\; \mathrm{kg}$ is in contact against the inner wall of a hollow cylindow cylindrical drum of radius $1 \;\mathrm{m}$. The coeffident of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ......$rad/s$ $\left(g-10 m / s^{2}\right)$

A vehicle of mass $200\,kg$ is moving along a levelled curved road of radius $70\,m$ with angular velocity of $0.2\,rad / s$. The centripetal force acting on the vehicle is $.........\,N$