A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1.	inclined at an angle of \(60^{\circ}\) from vertical.
2.	the mass is at the highest point.
3.	the wire is horizontal.
4.	the mass is at the lowest point.

When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) $$with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) $$and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:

Body \(\mathrm{A}\) of mass \(4m\) moving with speed \(u\) collides with another body \(\mathrm{B}\) of mass \(2m\) at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body \(\mathrm{A}\) is:

An object flying in the air with velocity \((20 \hat{i}+25 \hat{j}-12 \hat{k})\) suddenly breaks into two pieces whose masses are in the ratio of \(1:5.\) The smaller mass flies off with a velocity \((100 \hat{i}+35 \hat{j}+8 \hat{k})\)$\mathrm{}$. The velocity of the larger piece will be:
1. \( 4 \hat{i}+23 \hat{j}-16 \hat{k}\)
2. \( -100 \hat{i}-35 \hat{j}-8 \hat{k} \)
3. \( 20 \hat{i}+15 \hat{j}-80 \hat{k} \)
4. \( -20 \hat{i}-15 \hat{j}-80 \hat{k}\)

A particle of mass \(5m\) at rest suddenly breaks on its own into three fragments. Two fragments of mass \(m\) each move along mutually perpendicular directions with speed \(v\) each. The energy released during the process is:

An object of mass \(500~\text g\) initially at rest is acted upon by a variable force whose \(x\)-component varies with \(x\) in the manner shown. The velocities of the object at the points \(x=8~\text m\) and \(x=12~\text m\) would have the respective values of nearly:

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine?
(g = 10 m/s²)
1. 8.1 kW 
2. 10.2 kW
3. 12.3 kW
4. 7.0 kW