Question
State and explain Work-Energy theorem.
✓
Answer
Work done on a body is reflected as change in kinetic energy, according to Work-Energy theorem.
$\text{W}=\int\text{Fdx}=\int\text{m}\frac{\text{dv}}{\text{df}} \text{dx}$
$=\int\text{mv}\text{ dv}=\Big|\frac{1}{2}\text{mv}^2\Big|^\text{vf}_\text{vi}$
Work done $=\frac{1}{2}\text{m}(\text{v}^2_\text{f}-\text{v}_\text{i}^2)$
$=\frac{1}{2}\text{mv}_\text{f}^2-\frac{1}{2}\text{mv}_\text{i}^2$
Work done = Change in kinetic energy.
$\text{W}=\int\text{Fdx}=\int\text{m}\frac{\text{dv}}{\text{df}} \text{dx}$
$=\int\text{mv}\text{ dv}=\Big|\frac{1}{2}\text{mv}^2\Big|^\text{vf}_\text{vi}$
Work done $=\frac{1}{2}\text{m}(\text{v}^2_\text{f}-\text{v}_\text{i}^2)$
$=\frac{1}{2}\text{mv}_\text{f}^2-\frac{1}{2}\text{mv}_\text{i}^2$
Work done = Change in kinetic energy.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Characteristic X-rays may be used to identify the element from which they are being emitted. Can continuous X-rays be used for this purpose?
In a Quincke's experiment, the sound intensity has a minimum value I at a particular position. As the sliding tube is pulled out by a distance of 16.5mm, the intensity increases to a maximum of 9I. Take the speed of sound in air to be 330m/s.
- Find the frequency of the sound source.
- Find the ratio of the amplitudes of the two waves arriving at the detector assuming that it does not change much between the positions of minimum intensity and maximum intensity.
Velocity-time graph of a moving object is shown below. What is the acceleration of the object? Also draw displacement-time graph for the motion of the object.
A body oscillates with SHM according to the equation (in SI units), $
x=5 \cos [2 \pi t+\pi / 4] \text {. }
$
At $t=1.5 s$, calculate the (a) displacement, (b) speed and (c) acceleration of the body.
→x=5 \cos [2 \pi t+\pi / 4] \text {. }
$
At $t=1.5 s$, calculate the (a) displacement, (b) speed and (c) acceleration of the body.
The current in a long solenoid of radius R and having n turns per unit length is given by $\text{i}=\text{i}_0\sin\omega\text{t}.$ A coil having N turns is wound around it near the centre. Find
→- The induced emf in the coil.
- The mutual inductance between the solenoid and the coil.
Explain the difference between beats and interfrence.
Two vessels of the same size are at the same temperature. One of them holds 1kg of H2 gas and the other holds 1kg of N2 gas.
- Which of the vessels contains more molecules?
- Which of the vessels is under greater pressure and why?
- In which vessel is the average molecular speed greater? How many times greater?
One end of a rod of length 20cm is inserted in a furnace at 800K The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750K in the steady state. The temperature of the surrounding air is 300K. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant $\sigma=6.0\times10^{-8}\text{Wm}^{-2}\text{K}^{-4}.$
→The time period of a mass hanging from an ideal spring is 2 seconds. If along with it 2 kg if the mass is added and the time period becomes 3 seconds find the value of $m$.
→The gravitational potential energy of a two particle system is derived in this chapter as $\text{U}=-\frac{\text{Gm}_1\text{m}_2}{\text{r}}.$ Does it follow from this equation that the potential energy for $\text{r}=\infty$ must be zero? Can we choose the potential energy for $\text{r}=\infty.$ to be 20J and still use this formula? If no, what formula should be used to calculate the gravitational potential energy at separation r?
→