To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant $6.25\times {10}^3$ N/m. The maximum compression in the spring is:

To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed of 18.0 km/h on a rough road and colliding with a horizontally mounted spring of spring constant $2.5\times {10}^3 \mathrm{N}/\mathrm{m}$. If the coefficient of friction between road and tyre of the car, µ, to be 0.375. Maximum compression of the spring is:

The values of energy required to break one bond in DNA $\left({10}^{-20} \mathrm{J}\right)$ and the kinetic energy of an air molecule $\left({10}^{-21} \mathrm{J}\right)$ in eV respectively are:

An elevator can carry a maximum load of 1800 kg (elevator + passengers) is moving up with a constant speed of 2 m/s. The frictional force opposing the motion is 4000 N. The minimum power delivered by the motor to the elevator is:

In a nuclear reactor, a neutron of high speed (typically ${10}^7$ m/s) must be slowed to ${10}^3$ m/s so that it can have a high probability of interacting with isotope ${}_{92}{}^{235}\mathrm{U}$ and causing it to fission. The material making up the light nuclei, usually heavy water $\left({\mathrm{D}}_2\mathrm{O}\right)$ or graphite, is called a moderator. Find the fraction of the kinetic energy of the neutron lost by it in an elastic collision with light nuclei like deuterium.

The value of the daily intake of a human adult $\left({10}^7 \mathrm{J}\right)$ in kilocalories is:

The figure shows the variation of the kinetic energy of a block of mass m connected to a spring. Kinetic energy at the extreme position for this block of mass m will be:

A particle is released from a height of S above the surface of the earth. At a certain height, its kinetic energy is three times its potential energy. The distance from the earth's surface and the speed of the particle at that instant are respectively: 

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? $\left(g=10 m/s^2\right)$