A particle of mass m₁ is moving with a velocity v₁ and another particle of mass m₂ is moving with a velocity v₂. Both of them have the same momentum, but their kinetic energies are E₁ and E₂ respectively. If m₁ > m₂ then: 

1. $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}=\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}$

2. ${\mathrm{E}}_1>{\mathrm{E}}_2$

3. ${\mathrm{E}}_1={\mathrm{E}}_2$

4. ${\mathrm{E}}_1<{\mathrm{E}}_2$

The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is \(30^{\circ}\). One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is:

A stone is tied to a string of length 'l' is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed 'u'. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is:

1. $\sqrt{u^2-g\ell }$

2. $u-\sqrt{u^2-2g\ell }$

3. $\sqrt{2\mathrm{g}\ell }$

4. $\sqrt{2({\mathrm{u}}^2-\mathrm{g}\ell )}$

In semiconductors at room temperature:

The peak voltage in the output of a half-wave diode rectifier fed with a sinusoidal signal without a filter is \(10~\text V.\) The DC component of the output voltage is:
1. \(\dfrac{10}{\pi }~\text V\) 

2. \(10~\text V\) 

3. \(\dfrac{20}{\pi }~\text V\) 

4. \(\dfrac{10}{\sqrt{2}}~\text V\) 

A mass of \(0.5~\text{kg}\) moving with a speed of \(1.5~\text{m/s}\) on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50~\text{N/m}.\) The maximum compression of the spring would be:
                   
1.  \(0.12~\text{m}\) 
2.  \(1.5~\text{m}\) 
3.  \(0.5~\text{m}\) 
4.  \(0.15~\text{m}\) 

According to Einstein's photoelectric equation, the graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation is:

1.		2.
3.		4.