Identify the false' statement from the following

• Work-energy theorem is not independent of Newton's second law

• Work-energy theorem holds in all inertial frames

• Work done by friction over a closed path is zero

• No potential energy can be associated with friction

A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x =16 m is

• 45 J

• 30 J

• 70 J

• 135 J

33.

Two springs P and Q of force constants k_p and k_Q $\left({\mathrm{k}}_{\mathrm{Q}} = \frac{{\mathrm{k}}_{\mathrm{p}}}{2}\right)$ are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is

• E

• 2E

• $\frac{\mathrm{E}}{2}$

• $\frac{\mathrm{E}}{4}$

A rod of mass m and length l is made to stand at an angle of 60° with the vertical. Potential energy of the rod in this position is

• mgl

• $\frac{\mathrm{mgl}}{2}$

• $\frac{\mathrm{mgl}}{3}$

• $\frac{\mathrm{mgl}}{4}$

If an object of mass mis taken from the surface of earth (radius R) to a height 2R, then the work done is

• 2 mgR

• mgR

• $\frac{2}{3} \mathrm{mgR}$

• $\frac{3}{2} \mathrm{mgR}$

A particle of mass m carrying charge q is kept at rest in a uniform electric field E and then released. The kinetic energy gained by the particle, when it moves through a distance y is

• $\frac{1}{2} {\mathrm{qEy}}^2$

• qEy

• qEy²

• qE²y

A particle  acted upon by constant forces $4\hat{\mathrm{i}} + \hat{\mathrm{j}} - 3\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}$ is displaced from the point $\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ to the point $5\hat{\mathrm{i}} + 4\hat{\mathrm{j}} + \hat{\mathrm{k}}$. The total work done by the forces in SI unit is

• 20

• 40

• 50

• 30

Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg-wt. If they acquire the same kinetic energy in times t_A and t_B, then the ratio $\frac{{\mathrm{t}}_{\mathrm{A}}}{{\mathrm{t}}_{\mathrm{B}}}$ is

• $\frac{1}{2}$

• 2

• $\frac{2}{5}$

• $\frac{5}{6}$

The height of the dam, in a hydroelectric power station is 10 m. In order to generate 1 MW of electric power, the mass of water (in kg) that must fall per second on the blades of the turbines is

• 10⁶

• 10⁵

• 10³

• 10⁴

A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, the velocity of the ball is

• 50 ms^-1

• 9 ms^-1

• 90 ms^-1

• 60 ms^-1