A force $F$ acting on an object varies with distance $x$ as shown in the figure. The work done by the force in moving the object from $x = 0$ to $x = 8\,m$ is  ......... $J$

The energy required to accelerate a car from $10 \,m/s$ to $20\, m/s$ is how many times the energy required to accelerate the car from rest to $10\, m/s$

The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is

A body of mass $m$ moving with velocity $v$ collides head on with another body of mass  $2\, m$ which is initially at rest. The ratio of $K.E.$ of the colliding body before and  after collision will be 

A sphere of mass $0.1\,\,kg$  is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension this sphere hits a block of same mass at rest on a frictionless table. If the impact is elastic, then the kinetic energy of the block after the collision is ............. $\mathrm{J}$

A force $\vec F = (5\hat i + 3\hat j)\;N$is applied over a particle which displaces it from its original position to the point $\vec s = (2\hat i - 1\hat j)$m. The work done on the particle is.........$J$