A body constrained to move along the z-axis of a coordinate system is subjected to constant force given by $\overrightarrow{F}=-\hat{i}+2\hat{j}+3\hat{k}$ where $\hat{i}$, $\hat{j}$ and $\hat{k}$ are unit vectors along x-axis, y-axis and z-axis of the system respectively. The work done by this force in moving the body a distance of 4 m along the z-axis will be:

A pump on the ground floor of a building can pump up water to fill a tank of volume$30 m^3$ in 15 min. If the tank is 40 m above the ground and the efficiency of the pump is 30%. Then electric power consumed by the pump is:

$$\begin{gathered} \left(1\right) 44.4 kW \\ \left(2\right) 44 kW \\ \left(3\right) 40.7 kW \\ \left(4\right) 45 kW \end{gathered}$$ 

A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with a coefficient of kinetic friction = 0.1. The work done by the applied force in 10 s is:

Q.15 A raindrop falling from a height h above ground, attains a near-terminal velocity when it has fallen through a height (3/4)h. Which of the diagrams shown in figure correctly shows the change in kinetic and potential energy of the drop during its fall up to the ground?

Q.16 In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 m/s at 450 from a height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 m/${\mathrm{s}}^2$, the kinetic energy of the shotput when it just reaches the ground will be

The potential energy function for a particle executing linear simple harmonic motion is given by V(x) =$\frac{{\mathrm{kx}}^2}{2}$, where k is the force constant of the oscillator. For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy 1 J moving under this potential must turn back when it reaches:

$$\begin{gathered} 1. \mathrm{x}=\pm 1 \mathrm{m} \\ 2. \mathrm{x}=\pm 2 \mathrm{m} \\ 3. \mathrm{x}=\pm 3 \mathrm{m} \\ 4. \mathrm{x}=\pm 4 \mathrm{m} \end{gathered}$$

Which one of the following statement is wrong?

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. The ratio of their speeds is:

$$\begin{gathered} \left(1\right) 13.5:1 \\ \left(2\right) 1:1 \\ \left(3\right) 1:13.5 \\ \left(4\right) 2:1 \end{gathered}$$

($m_e$ = $9.31\times {10}^{-31} kg$, $m_p$ = $1.67\times {10}^{-27} kg$, 1 eV = $1.60\times {10}^{-19} kg$).

A raindrop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until, at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey?

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

A body of mass 0.5 kg travels in a straight line with velocity $\mathrm{v}={\mathrm{ax}}^{3/\mathrm{2 }}$where $\mathrm{a}=5 {\mathrm{m}}^{-1/2} {\mathrm{s}}^{-1}$. What is the work done by the net force during its displacement from x = 0 to x = 2 m?

A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. How much work does she do against the gravitational force?

A family uses 8 kW of power. Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square meter. If 20% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?

$$\begin{gathered} 1. 180 m^2 \\ 2. 150 m^2 \\ 3. 200 m^2 \\ 4. 300 m^2 \end{gathered}$$

A 1 kg block situated on a rough incline is connected to a spring of spring constant $100 N m^{-1}$ as shown in the figure. The block is released from rest with the spring in the unstretched position. The block moves 10 cm down the incline before coming to rest. The coefficient of friction between the block and the incline is:

(Assume that the spring has a negligible mass and the pulley is frictionless.)

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down at a uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?

A string is used to pull a block of mass m vertically up by a distance h at a constant acceleration $\frac{\mathrm{g}}{3}$. The work done by the tension in the string is

A body constrained to move in the z-direction is subjected to a force given by $\overrightarrow{\mathrm{F}}=(3\hat{\mathrm{i}}-10\hat{\mathrm{j}}+5\hat{\mathrm{k}}) \mathrm{N}$. What is the work done by the force in moving the body through a distance of 5m along the z-axis?

A man carries a load on his head through a distance of 5 m. The maximum amount of work is done when he:

A particle is displaced from a position $(2\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$ metre to another position $(3\hat{\mathrm{i}}+2\hat{\mathrm{j}}-2\hat{\mathrm{k}})$ metre under the action of force $(2\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$N. Work done by the force is

Work done by frictional force

Two bodies of masses m₁ and m₂ have same kinetic energy. The ratio of their momentum is

Two bodies of masses m₁ and m₂ have same momentum. The ratio of their KE is

Two bodies of masses m₁ and m₂ are moving with same kinetic energy. If P₁ and P₂ are their respective momentum, the ratio $\frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}$ is equal to

A particle moves along X-axis from x=0 to x=1 m under the influence of a force given by $\mathrm{F}=3{\mathrm{x}}^2+2\mathrm{x}-10$. Work done in the process is

Under the action of a force, a 2 kg body moves such that its position x as a function of time t is given by $\mathrm{x}=\frac{{\mathrm{t}}^2}{3}$, where x is in metre and t in second. The work done by the force in first two seconds is

KE acquired by a mass m intravelling a certain distance d, starting from rest, under the action of a constant force F is

The total work done on a particle is equal to the change in its kinetic energy. This is applicable 

Potential energy is defined:

A spring with spring constants k when compressed by 1 cm, the potential energy stored is U. If it is further compressed by 3 cm, then change in its potential energy is

Two springs have force constant K₁ and K₂ (K₁>K₂). Each spring is extended by same force F. If their elastic potential energy are E₁ and E₂ then $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}$ is