\(y=3\sin\pi\Big(\frac t2-\frac x4\Big),\) represents an equation of a progressive wave, where \(t\) is in second and \(x\) is in meter. The distance travelled by the wave in \(5\) seconds is:
1. \(8\) m
2. \(10\) m
3. \(5\) m
4. \(32\) m

A body of mass \(m_1=4~\mathrm{kg}\) moves at \(5i~\mathrm{m/s}\) and another body of mass \(m_2=2~\mathrm{kg}\) moves at \(10i~\mathrm{m/s}\). The kinetic energy of the centre of mass is:
1. \(\frac{200}{3}~\text J\)
2. \(\frac{500}{3}~\text J\)
3. \(\frac{400}{3}~\text J\)
4. \(\frac{800}{3}~\text J\)

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. \(8~\mathrm{kg-m^2}\) 

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