Two particles with mass m_1 = 16 kg and m_2 | vedclass

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

Question

(C) The potential energy stored in the compressed spring is converted into the kinetic energy of the particles in the center of mass frame.Let the rel

Vedclass · Accepted Answer

$1.88$

Vedclass · Answer

(C) The potential energy stored in the compressed spring is converted into the kinetic energy of the particles in the center of mass frame.Let the relative velocity of separation be $v_{rel}$.The reduced mass of the system is $\mu = \frac{m_1 m_2}{m_1 + m_2} = \frac{16 	imes 2}{16 + 2} = \frac{32}{18} = \frac{16}{9} \ kg$.The energy conservation equation is $\frac{1}{2} kx^2 = \frac{1}{2} \mu v_{rel}^2$.Given $k = 100 \ Nm^{-1}$ and $x = 25 \ cm = 0.25 \ m = \frac{1}{4} \ m$.Substituting the values: $\frac{1}{2} 	imes 100 	imes (\frac{1}{4})^2 = \frac{1}{2} 	imes \frac{16}{9} 	imes v_{rel}^2$.$100 	imes \frac{1}{16} = \frac{16}{9} 	imes v_{rel}^2$.$v_{rel}^2 = \frac{100}{16} 	imes \frac{9}{16} = \frac{900}{256}$.$v_{rel} = \sqrt{\frac{900}{256}} = \frac{30}{16} = 1.875 \ ms^{-1}$.Rounding to two decimal places,we get $v_{rel} \approx 1.88 \ ms^{-1}$.

Similar Questions

Two springs of spring constants $K$ and $2K$ are stretched by the same force. If $W_{1}$ and $W_{2}$ are the energies stored in them respectively,then:

When a spring is stretched by $2 \ cm$,the potential energy stored is $U$. If it is stretched by $10 \ cm$,the potential energy stored will be:

$A$ mechanical system consists of two springs with stiffness coefficients $k_1$ and $k_2$ connected in series. The minimum work to be performed on the system to stretch it by a total displacement $\Delta$ is

$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

$A$ block of mass $M$ moving on a frictionless horizontal surface collides with a spring of spring constant $K$ and compresses it by a length $L$. The maximum momentum of the block during the collision process is

Vedclass Test Series

Exam Paper Generator

Online Exam Module