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. | 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 |
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
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. \(n=3,l=0,m=0,s=+\frac12\)