The kinetic energy of a person is just half of the kinetic energy of a boy whose mass is just half of that person. If the person increases his speed by \(1~\text{m/s},\) then his ​​​​​​​kinetic energy equals to that of the boy, then the initial speed of the person was:
1. \(\left( \sqrt{2}+1 \right)~\text{m/s}\)
2. \(\left( 2+\sqrt{2} \right)~\text{m/s}\)
3. \(2\left( 2+\sqrt{2} \right)~\text{m/s}\)
4. none of the above

\(250\) N force is required to raise \(75\) kg mass from a pulley. If the rope is pulled \(12\) m, then the load is lifted to \(3\) m. The efficiency of the pulley system will be: 
1. \(25\text{%}\)
2. \(33.3\text{%}\)
3. \(75\text{%}\)
4. \(90\text{%}\)

If the kinetic energy of a body is increased by
\(300\)%, then the percentage change in momentum will be:
1. \(100\)%
2. \(150\)%
3. \(265\)%
4. \(73.2\)%

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. ${\mathrm{E}}_1<{\mathrm{E}}_2$