Two blocks with masses 100 text{ g} and 200 t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a spring-mass system in equilibrium, the spring force balances the gravitational force: $kx = mg$, where $x$ is the extension of the spring.Th

Vedclass · Accepted Answer

$3E$

Vedclass · Answer

(C) For a spring-mass system in equilibrium, the spring force balances the gravitational force: $kx = mg$, where $x$ is the extension of the spring.Thus, the extension is $x = \frac{mg}{k}$.The elastic potential energy $U$ stored in the spring is given by $U = \frac{1}{2}kx^2$.Substituting the value of $x$, we get $U = \frac{1}{2}k\left(\frac{mg}{k}ight)^2 = \frac{m^2g^2}{2k}$.From this expression, we see that $U \propto \frac{m^2}{k}$.Given $m_{A} = 100 	ext{ g}$, $m_{B} = 200 	ext{ g}$, and $4k_{A} = 3k_{B}$, we can write the ratio of energies as:$\frac{U_{A}}{U_{B}} = \left(\frac{m_{A}}{m_{B}}ight)^2 \cdot \left(\frac{k_{B}}{k_{A}}ight)$.Substituting the values: $\frac{E}{U_{B}} = \left(\frac{100}{200}ight)^2 \cdot \left(\frac{4}{3}ight) = \left(\frac{1}{2}ight)^2 \cdot \left(\frac{4}{3}ight) = \frac{1}{4} \cdot \frac{4}{3} = \frac{1}{3}$.Therefore, $U_{B} = 3E$.

Similar Questions

$A$ spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k'$. Then they are connected in parallel and the force constant is $k''$. Then $k':k''$ is

When the acceleration of the $5\ kg$ block is $2\ m/s^2$ as shown in the figure,what will be the acceleration of the $15\ kg$ block? (in $m/s^2$)

The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now, the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

$A$ body of mass $m$ is suspended from an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

Vedclass Test Series

Exam Paper Generator

Online Exam Module