Question:
A mass of $ 400\,g $ and a mass of $ 100\,g $ have same $ KE $ , then the ratio of their momentums will be
A mass of $ 400\,g $ and a mass of $ 100\,g $ have same $ KE $ , then the ratio of their momentums will be
Updated On: Jun 20, 2022
- $ 2 : 1 $
- $ 1 : 2 $
- $ 1 : 3 $
- $ 3: 1 $
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
$\frac{p_{1}}{p_{2}}=\sqrt{\frac{2 m_{1} E_{1}}{2 m_{2} E_{2}}}=\sqrt{\frac{2 m_{1}}{2 m_{2}}}$
$\left[\right.$ As $\left.E_{1}=E_{2}\right]$
We have
$\frac{p_{1}}{p_{2}}=\sqrt{\frac{2 m_{1}}{2 m_{2}}}=\sqrt{\frac{m_{1}}{m_{2}}}$
$\therefore \frac{p_{2}}{p_{1}}=\sqrt{\frac{m_{2}}{m_{1}}}$
Here, $m_{2}=400 g , m_{1}=100 g$
$\therefore \frac{p_{2}}{p_{1}}=\sqrt{\frac{400}{100}}=\frac{\sqrt{4}}{1}=\frac{2}{1}$
$\Rightarrow p_{2}: p_{1}=2: 1$
$\left[\right.$ As $\left.E_{1}=E_{2}\right]$
We have
$\frac{p_{1}}{p_{2}}=\sqrt{\frac{2 m_{1}}{2 m_{2}}}=\sqrt{\frac{m_{1}}{m_{2}}}$
$\therefore \frac{p_{2}}{p_{1}}=\sqrt{\frac{m_{2}}{m_{1}}}$
Here, $m_{2}=400 g , m_{1}=100 g$
$\therefore \frac{p_{2}}{p_{1}}=\sqrt{\frac{400}{100}}=\frac{\sqrt{4}}{1}=\frac{2}{1}$
$\Rightarrow p_{2}: p_{1}=2: 1$
Was this answer helpful?
0
0
Top UPSEE Physics Questions
- Lenz?s law is consequence of the law of conservation of
- Two coherent monochromatic light beams of intensities ratio 1 : 4 are superposed. The ratio of maximum and minimum intensities in the resulting beam will be
- A convex lens of focal length 10 cm and refractive index 1.5 is dipped in a liquid of refractive index 1.75. It will behave as
- Two beams of red and violet colour are made to pass separately through a prism with angle of prism $60^{\circ}$. In the position of minimum deviation, the angle of refraction will be:
- ?Lumen? is the unit of
View More Questions
Top UPSEE work, energy and power Questions
- A particle of mass $ 100\,g $ is thrown vertically upwards with a speed of $5m/s $ . the work done by the force of gravity during the time the particle goes up is
- A particle is moving in translatory motion. If momentum of the particle decreases by $10\%$, kinetic energy will decrease by
- A small bead of mass $M$ slides on a smooth wire that is bent in a circle of radius $R$. It is released at the top of the circular part of the wire (point A in the figure) with a negligibly small velocity. Find the height H where the bead will reverse direction.
Top UPSEE Questions
- The movement of Pollen tube is:
- Let P be a $2 \times 2$ matrix such that [1 0] P = $ - \frac{1}{\sqrt{2}} [ 1 1]$ and $[0 1] P = \frac{1}{\sqrt{2}} [- 1 1]$ . If 0 and I denote the zero and identity matrices of order 2, respectively, then which of the following options is CORRECT ?
- If det $\begin{bmatrix}1&1&2\\ 2&4&9\\ t&t^{2}&1+t^{3}\end{bmatrix} = 0 $ , then the values of t are
- Which one of the following group is nutritionally essential amino acids?
- Let $x^2 + \alpha x + \beta = 0$ the equation whose roots are the negatives of the roots of $x^2 + 7x - 2 = 0$ then the value of $\alpha + \beta$ is
View More Questions
Concepts Used:
Work, Energy and Power
Work:
- Work is correlated to force and the displacement over which it acts. When an object is replaced parallel to the force's line of action, it is thought to be doing work. It is a force-driven action that includes movement in the force's direction.
- The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.
Energy:
- A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
- There are two types of mechanical energy such as; Kinetic and potential energy.
Read More: Work and Energy
Power:
- Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
- Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.