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 different kinetic energies are E₁ and E₂ respectively. If m₁ > m₂ then 

(1) E₁ < E₂

(2) $\frac{E_1}{E_2}=\frac{m_1}{m_2}$

(3) E₁ > E₂

(4) E₁ = E₂

Four particles are given, having same momentum. Which one has maximum kinetic energy- 

(1) Proton

(2) Electron

(3) Deutron

(4) α-particles

An object of mass 3m splits into three equal fragments. Two fragments have velocities $v\hat{j}$ and $v\hat{i}$. The velocity of the third fragment is 

(1) $v(\hat{j}-\hat{i})$

(2) $v(\hat{i}-\hat{j})$

(3) $-v(\hat{i}+\hat{j})$

(4) $\frac{v(\hat{i}+\hat{j})}{\sqrt{2}}$

A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. The maximum compression in the spring is x then-

(1) $mgh=\frac{1}{2}k{x}^2$

(2) $mg(h+x)=\frac{1}{2}k{x}^2$

(3) $mgh=\frac{1}{2}k{(x+h)}^2$

(4) $mg(h+x)=\frac{1}{2}k{(x+h)}^2$

A spherical ball of mass \(20\) kg is stationary at the top of a hill of height\(100\) m. It slides down a smooth surface to the ground, then climbs up another hill of height \(30\) m and finally slides down to a horizontal base at a height of \(20\) m above the ground. The velocity attained by the ball is: 
1. \(10 \) m/s
2. \(10 \sqrt{30} \) m/s
3. \(40 \) m/s
4. \(20 \) m/s

The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is 

(1) Zero

(2) $\frac{M{L}^2}{K}$

(3) $\sqrt{MK}L$

(4) $\frac{K{L}^2}{2M}$

A body of mass m accelerates uniformly from rest to v₁ in time t₁. As a function of time t, the instantaneous power delivered to the body is 

(1) $\frac{m{v}_{1}t}{t_1}$

(2) $\frac{m{v}_1^{2}t}{t_1}$

(3) $\frac{m{v}_1{t}^2}{t_1}$

(4) $\frac{m{v}_1^{2}t}{t_1^2}$

A weight lifter lifts 300 kg from the ground to a height of 2 meter in 3 second. The average power generated by him is 

(1) 5880 watt

(2) 4410 watt

(3) 2205 watt

(4) 1960 watt

The average power required to lift a 100 kg mass through a height of 50 metres in approximately 50 seconds would be 

(1) 50 J/s

(2) 5000 J/s

(3) 100 J/s

(4) 980 J/s

The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is (g = 10 m/s²) 

(1) 40 kW

(2) 80 kW

(3) 400 kW

(4) 960 kW