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? $\left(g=10\right)$ $m/s^2$

1.	12.3 kW	2.	7.0 kW
3.	10.2 kW	4.	8.1 kW

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

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

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.

1.  $\frac{1}{9}$

2.  $\frac{8}{9}$

3.  $\frac{9}{8}$

4.  $\frac{1}{8}$

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:
1. \(59000\) W
2. \(44000\) W
3. \(11000\) W
4. \(22000\) W

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 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:

1.   3.5 m

2.   2.0 m

3.   1.5 m

4.   2.5 m

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 \(6.25\times 10^3~{\mathrm{N/m}}\). The maximum compression in the spring is:
1. \(3\) m
2. \(0.2\) m
3. \(1\) m
4. \(2\) m

A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_0$ 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. If the connecting string is cut at point C, the trajectory of bob is:

1.   Straight line

2.   Circular 

3.   Projectile 

4.   Can't be determined

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 \(\frac{K_B}{K_C}\) ${\mathrm{}}_{}$at points \(\mathrm{B}\) and \(\mathrm{C}\) is:
${\mathrm{}}_{}$

                  
1. \(1:3\)
2. \(3:1\)
3. \(1:5\)
4. \(5:1\)