An elevator can carry a maximum load of \(1800~\text{kg}\) (elevator + passengers), moving up with a constant speed of \(2~\text{m/s}.\) The frictional force opposing the motion is \(4000~\text{N}.\) The minimum power delivered by the motor to the elevator is:
1. \(59000~\text{W}\) 
2. \(44000~\text{W}\) 
3. \(11000~\text{W}\) 
4. \(22000~\text{W}\) 

In a nuclear reactor, a neutron of high speed (typically \(\left(10\right)^{7}\) m/s) must be slowed to \(\left(10\right)^{3}\) m/s so that it can have a high probability of interacting with isotope \(^{235}_{92}U\) and causing it to fission. The material making up the light nuclei, usually heavy water \(\left(D_{2} O\right)\) 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.

1.  \(\dfrac{1}{9}\)

2.  \(\dfrac{8}{9}\)

3.  \(\dfrac{9}{8}\)

4.  \(\dfrac{1}{8}\)

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

1.   24 k cal

2.   2.4 kcal

3.   2400 kcal

4.   240 kcal

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:

1. $k{x}_m^2$

2. $\frac{k{x}_m^2}{2}$

3. $\frac{k{x}_m^2}{4}$

4. Zero

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? $\left(g=10\right)$ $m/s^2$

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

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 \(1000~\text{kg}\) moving with a speed of \(18~\text{km/h}\) on a rough road and colliding with a horizontally mounted spring of spring constant \(2.5\times 10^3~\text{N/m}\)$\mathrm{}$. If the coefficient of friction between road and tyre of the car, \(\mu\), to be \(0.375\). Maximum compression of the spring is:
1. \(3.5~\text{m}\)
2. \(2.0~\text{m}\)
3. \(1.5~\text{m}\)
4. \(2.5~\text{m}\)

A bob of mass m is suspended by a light string of length \(L.\) It is imparted a horizontal velocity \(v_0\) at the lowest point \(A\) such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the ratio of the kinetic energies \(\dfrac{K_B}{K_C}\) ${\mathrm{}}_{}$at points \({B}\) and \({C}\) is: