A wheel of radius \(0.4~\mathrm{m}\) can rotate freely about its axis as shown in the figure. A string is wrapped over its rim, and a mass of \(4~\mathrm{kg}\) is hung. An angular acceleration of \(8~\mathrm{rad/s^2}\) is produced in it due to the torque. Then, moment of inertia of the wheel is: (Take \(g=10\) ms-2)
1. \(2~\mathrm{kg-m^2}\)
2. \(1~\mathrm{kg-m^2}\)
3. \(4~\mathrm{kg-m^2}\)
4. \(8~\mathrm{kg-m^2}\)
1. \(2~\mathrm{kg-m^2}\)
2. \(1~\mathrm{kg-m^2}\)
3. \(4~\mathrm{kg-m^2}\)
4. \(8~\mathrm{kg-m^2}\)
| 1. | both will reach with same speed |
| 2. | both will reach with same acceleration |
| 3. | both will reach in the same time |
| 4. | none of the above |
1. \(60.25^\circ\)
2. \(63.90^\circ\)
3. \(26.12^\circ\)
4. \(30.00^\circ\)
A coin is dropped in a lift. It takes time \(t_1\) to reach the floor when the lift is stationary. It takes time \(t_2\) when the lift is moving up with constant acceleration. Then, what is the relationship between \(t_1\) and \(t_2 ?\)
1. \(t_1>t_2\)
2. \(t_2>t_1\)
3. \(t_1=t_2\)
4. \(t_1>>t_2\)
The engine of a jet aircraft applies a thrown force of \(10^5\) N during takeoff and causes the plane to attain a velocity of \(1\) km/s in \(10\) s. The mass of the plane is:
1. \(10^2\) kg
2. \(10^3\) kg
3. \(10^4\) kg
4. \(10^5\) kg
1. \(-20\) N
2. \(-0.2\) N
3. \(0.2\) N
4. \(20\) N
1. constant
2. proportional to \(x\)
3. proportional to \(x^2\)
4. inversely proportional to \(x\)
2. \(20\)
3. \(30\)
4. \(40\)
A hollow sphere of volume \(V\) is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?
1. \(\frac V2\)
2. \(\frac V3\)
3. \(\frac V4\)
4. \(V\)
Which one of the following sets of quantum numbers represents the highest energy level in an atom?
1. \(n=4,l=0,m=0,s=+\frac12\)
2. \(n=3,l=1,m=1,s=+\frac12\)
3. \(n=3,l=2,m=-2,s=+\frac12\)
4. \(n=3,l=0,m=0,s=+\frac12\)
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