A solid sphere and a hollow sphere of the same material and of the same size can be distinguished without weighing:

1.	by determining their moments of inertia about their coaxial axes
2.	by rolling them simultaneously on an inclined plane
3.	by rotating them about a common axis of rotation
4.	by applying equal torque on them

Point masses \(1,\) \(2,\) \(3\) and \(4\) kg are lying at the points \((0,0,0),\) \((2,0,0),\) \((0,3,0)\) and \((-2,-2,0)\) respectively. The moment of inertia of this system about the X-axis will be:
1. \(43~\mathrm{kg-m^2}\) 
2. \(34~\mathrm{kg-m^2}\) 
3. \(27~\mathrm{kg-m^2}\) 
4. \(72~\mathrm{kg-m^2}\) 

The radius of gyration of a body about an axis at a distance \(6~\mathrm{cm}\) from its centre of mass is \(10~\mathrm{cm}\). Then, its radius of gyration about a parallel axis through its centre of mass will be:
1. \(80~\mathrm{cm}\) 
2. \(8~\mathrm{cm}\) 
3. \(0.8~\mathrm{cm}\) 
4. \(80~\mathrm{m}\) 

A galvanometer can be changed into an ammeter by using:

A bullet of mass \(20\) g and moving with \(600\) m/s collides with a block of mass \(4\) kg hanging with the string. What is the velocity of a bullet when it comes out of the block, if the block rises to height \(0.2\) m after collision?
1. \(200\) m/s
2. \(150\) m/s
3. \(400\) m/s
4. \(300\) m/s

Voltage in the secondary coil of a transformer does not depend upon:

In Carnot, engine efficiency is \(40\text{%}\), at hot reservoir temperature \(T\). For \(50\text{%}\) efficiency, what will be the temperature of the hot reservoir?
1. \(\frac TS\)
2. \(\frac{2T}{5}\)
3. \(6T\)
4. \(\frac{6T}{5}\)

A ball of mass \(2\) kg moving with velocity \(3\) m/s, collides with spring of natural length \(2\) m and force constant \(144\) N/m. What will be the length of the compressed spring?
1. \(2\) m
2. \(1.5\) m
3. \(1\) m
4. \(0.5\) m

A proton moving vertically downward enters a magnetic field pointing towards the north. In which direction the proton will deflect?
1. east
2. west
3. north
4. south

Induced emf in the coil depends upon: