A shell of mass 200g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is -

1. 100 $m{s}^{-1}$

2. 80 $m{s}^{-1}$

3. 40 $m{s}^{-1}$

4. 120 $m{s}^{-1}$

The potential energy U between two molecules as a function of the distance X between them has been shown in the figure. The two molecules are -

1. Attracted when x lies between A and B and are repelled when X lies between B and C

2. Attracted when x lies between B and C and are repelled when X lies between A and B

3. Attracted when they reach B

4. Repelled when they reach B

The points of maximum and minimum attraction in the curve between potential energy (U) and distance (r) of a diatomic molecules are respectively -

(1) S and R

(2) T and S

(3) R and S

(4) S and T

K is the force constant of a spring. The work done in increasing its extension from $l_1$ to $l_2$ will be

1. $K\left(l_2-l_1\right)$                             

2. $\frac{K}{2}\left(l_2+l_1\right)$

3. $K\left(l_2^2-l_1^2\right)$                           

4. $\frac{K}{2}\left(l_2^2-l_1^2\right)$

An electron is accelerated through a potential difference of 200 volts. If e/m for the electron be $1.6\times {10}^{11}$ coulomb/kg, the velocity acquired by the electron will be

(1) $8\times {10}^6 \mathrm{m}/\mathrm{s}$                           

(2) $8\times {10}^5 \mathrm{m}/\mathrm{s}$

(3) $5.9\times {10}^6 \mathrm{m}/\mathrm{s}$                         

(4) $5.9\times {10}^5 \mathrm{m}/\mathrm{s}$

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine?
(g = 10 m/s²)
1. 8.1 kW 
2. 10.2 kW
3. 12.3 kW
4. 7.0 kW

A block of mass \(M\) is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of \(k.\) The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:
1. \(Mg/k\)
2. \(2Mg/k\)
3. \(4Mg/k\)
4. \(Mg/2k\)

A body of mass 1 kg is thrown upwards with a velocity $20 {\mathrm{ms}}^{-1}.$ It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? $\left(\mathrm{g}=10 {\mathrm{ms}}^{-2}\right)$

1. 20 J                               
2. 30 J
3. 40 J                               
4. 10 J

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of $12 {\mathrm{ms}}^{-1}$ and 2 kg second part moving with a velocity of $8 {\mathrm{ms}}^{-1}.$ If the third part flies off with a velocity of $4 {\mathrm{ms}}^{-1},$ its mass would be 

1. $5 \mathrm{kg}$                                          
2. $7 \mathrm{kg}$
3. $17 \mathrm{kg}$                                         
4. $3 \mathrm{kg}$

A particle of mass M starting from rest undergoes uniform acceleration. If the speed acquired in time T is v, the power delivered to the particle is 

1. $\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$                                 

2. $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$

3. $\frac{{\mathrm{Mv}}^2}{{\mathrm{T}}^2}$                                   

4. $\frac{1}{2}\frac{{\mathrm{Mv}}^2}{\mathrm{T}}$