A particle moves with the velocity $\overrightarrow{\mathrm{v}}=(5\hat{\mathrm{i}}+2\hat{\mathrm{j}}-\hat{\mathrm{k}}){\mathrm{ms}}^{-1}$ under the influence of a constant force, $\overrightarrow{\mathrm{F}}(2\hat{\mathrm{i}}+5\hat{\mathrm{j}}-10\hat{\mathrm{k}})$ N. The instantaneous power applied is

1. 5 W

2. 10 W

3. 20 W

4. 30 W

A body is projected from ground obliquely. During downward motion, power delivered by gravity to it

1. Increases

2. Decreases

3. Remains constant

4. First decreases and then becomes constant

A body of mass m accelerates uniformly from rest to velocity v₁ in time interval T₁. The instantaneous power delivered to the body as a function of time t is

1. $\frac{{\mathrm{mv}}_1^2}{{\mathrm{T}}_1^2}\mathrm{t}$

2. $\frac{{\mathrm{mv}}_1}{{\mathrm{T}}_1^2}\mathrm{t}$

3. ${\left(\frac{{\mathrm{mv}}_1}{\mathrm{T}}\right)}^2\mathrm{t}$

4. $\frac{{\mathrm{mv}}_1^2}{{\mathrm{T}}_1}{\mathrm{t}}^2$

The power of a pump, which can pump 500 kg of water to height 100 m in 10 s is

1. 75 kW

2. 25 kW

3. 50 kW

4. 500 kW

A U-238 nucleus originally at rest, decays by emitting an $\mathrm{\alpha }$-particle, say with a velocity of v m/s. The recoil velocity (in ms^-1) of the residual nucleus is

1. $\frac{4\mathrm{v}}{238}$

2. $-\frac{4\mathrm{v}}{238}$

3. $\frac{\mathrm{v}}{4}$

4. $-\frac{4\mathrm{v}}{234}$

An object of mass 80 kg moving with velocity 2 ms^-1 hit by collides with another object of mass 20 kg moving with velocity 4 ms^-1. Find the loss of energy assuming a perfectly inelastic collision

1. 12 J

2. 24 J

3. 30 J

4. 32 J

Particle A makes a perfectly elastic collision with another particle B at rest. They fly apart in opposite directions with equal speeds. If their masses are m_A and m_B respectively, then

1. 2m_A = m_B 

2. 3m_A = m_B

3. 4m_A = m_B

4. $\sqrt{3}$m_A = m_B

A body of mass 10 kg moving with speed of 3 ms^-1 collides with another stationary body of mass 5 kg. As a result, the two bodies stick together. The KE of composite mass will be

1. 30 J

2. 60 J

3. 90 J

4. 120 J

Select the false statement 

1. In elastic collision, KE is not conserved during the collision

2. The coefficient of restitution for a collision between two steel balls lies between 0 and 1

3. The momentum of a ball colliding elastically with the floor is conserved

4. In an oblique elastic collision between two identical bodies with one of them at rest initially, the final velocities are perpendicular

A bullet of mass m moving with a velocity u strikes a block of mass M at rest and gets embedded in the block. The loss of kinetic energy in the impact is

1. $\frac{1}{2}{\mathrm{mMu}}^2$

2. $\frac{1}{2}(\mathrm{m}+\mathrm{M}){\mathrm{u}}^2$

3. $\frac{{\mathrm{mMu}}^2}{2(\mathrm{m}+\mathrm{M})}$

4. $\left(\frac{\mathrm{m}+\mathrm{M}}{2\mathrm{mM}}\right){\mathrm{u}}^2$