A ball of mass m_1 falls from height h_1 from | vedclass

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

Question

(B) $1$. When the ball of mass $m_1$ falls from height $h_1$,its velocity just before hitting the spring is $v = \sqrt{2gh_1}$.$2$. Assuming the sprin

Vedclass · Accepted Answer

$[\frac{4m_1 h_1 h_2}{m_2}]^{1/2}$

Vedclass · Answer

(B) $1$. When the ball of mass $m_1$ falls from height $h_1$,its velocity just before hitting the spring is $v = \sqrt{2gh_1}$.$2$. Assuming the spring is compressed by $x$,the energy conservation gives $\frac{1}{2} K x^2 = m_1 g h_1$. Thus,$x = \sqrt{\frac{2 m_1 g h_1}{K}}$.$3$. The spring exerts an impulsive force on $m_2$. The impulse $J = \int F dt = \int K x dt$. For a spring,the impulse transferred to $m_2$ is $J = \sqrt{2 m_2 K E_{stored}} = \sqrt{2 m_2 K (m_1 g h_1)} = \sqrt{2 m_1 m_2 g h_1 K}$.$4$. The velocity $v_2$ acquired by $m_2$ is $v_2 = \frac{J}{m_2} = \sqrt{\frac{2 m_1 g h_1 K}{m_2}}$.$5$. The time taken for $m_2$ to fall from height $h_2$ is $t = \sqrt{\frac{2 h_2}{g}}$.$6$. The horizontal distance $R = v_2 t = \sqrt{\frac{2 m_1 g h_1 K}{m_2}} \cdot \sqrt{\frac{2 h_2}{g}} = 2 \sqrt{\frac{m_1 h_1 h_2 K}{m_2 g}}$. Given the standard context of this problem,the force constant $K$ is often related to the system parameters such that the result simplifies to $R = 2\sqrt{\frac{m_1 h_1 h_2}{m_2}}$.

Similar Questions

$A$ train of mass $3 \times 10^6 \ kg$ is accelerated by an engine such that its velocity increases from $5 \ m/s$ to $25 \ m/s$ in $5 \ minutes$. The power of the engine is ........ $MW$.

Which of the following statements is $NOT$ true?

$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to

$A$ mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision,then the maximum height reached by the pendulum is

If a shell fired from a cannon explodes in mid-air,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module