Work, Energy and Power

A toy rocket of mass 0.1 kg has a small fuel of mass 0.02 kg, which it burns out in 3s. Starting from rest on a horizontal smooth track, it get a speed of 20 ms^-1 after the fuel is burn out. The energy content per unit mass of the fuel is (Ignore the small mass variation of the rocket during fuel burning)

• 20 J/kg

• 100 J/Kg

• 1000 J/kg

• 400 J/kg

Three points charges q, -2q and -2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{2{\mathrm{q}}^2}{\mathrm{a}}$

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{{\mathrm{q}}^2}{2\mathrm{a}}$

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{8\mathrm{q}}{{\mathrm{a}}^2}$

• 0

A wooden ball of density ρ is immersed in water of density σ to depth h and then released, then the height x above the surface of water upto which the ball jumps out of water is equal to

• $\left(\frac{\mathrm{\rho }}{\mathrm{\sigma }} - 1\right)\mathrm{h}$

• $\left(\frac{\mathrm{\sigma }}{\mathrm{\rho }} - 1\right)\mathrm{h}$

• $\left(1 - \frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)\mathrm{h}$

• $\left(1 - \frac{\mathrm{\rho }}{\mathrm{\sigma }}\right)\mathrm{h}$

A ball is dropped to the ground from a height of 2 m. The coefficient of restitution is 0.6. To what height will the ball rebound ?

• 0.41 m

• 0.9 m

• 0.72 m

• 0.28 m

A lift of mass 1000 kg is descending with a speed of 6 ms^-1 . Suddenly the cable of the lift begins to slip and it falls with a constant acceleration a = $\frac{9}{6}$m / s² . What is the kinetic energy of the lift after falling a distance 15 m ?

• 121.3 kJ

• 155.6 kJ

• 147.4 kJ

• 134.1 kJ

Two spherical bodies of mass M and 5 M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller bodyjust before collision, is

• 1.5 R

• 2.5 R

• 4.5 R

• 7.5  R

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

• increase

• remain unchanged

• decrease

• first increase then decrease

The kinetic energy of an electron, which is accelerated in the potential difference of l00 V, is

• 1.6 × 10^-17 J

• 1.6 × 10^-14 J

• 1.6 × 10^-10 J

• 1.6 × 10^-8 J

When a force is applied on a moving body, its motion is retarded. Then the work done is

• positive

• negative

• zero

• positive and negative

A particle is displaced from a position $\left(2\stackrel{\wedge }{\mathrm{i}} - \stackrel{\wedge }{\mathrm{j}} + \stackrel{\wedge }{\mathrm{k}}\right)$ to another position $\left(3\stackrel{\wedge }{\mathrm{i}} + 2\stackrel{\wedge }{\mathrm{j}} - 2\stackrel{\wedge }{\mathrm{k}}\right)$ under the action of the force of $\left(2\stackrel{\wedge }{\mathrm{i}} + \stackrel{\wedge }{\mathrm{j}} - \stackrel{\wedge }{\mathrm{k}}\right)$. The work done by the force in an arbitrary unit is

• 8

• 10

• 12

• 16