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

$A$ ball of mass $0.2 \,kg$ is thrown vertically down from a height of $10 \,m$. It collides with the floor and loses $50 \%$ of its energy and then rises back to the same height. The value of its initial velocity is

$A$ body of mass $5 \,kg$ falls from a height of $30 \,m$. If all its mechanical energy is converted into heat,then the heat produced will be ........ $cal$.

$A$ truck pulls a mass of $1200 \ kg$ at a constant speed of $10 \ m/s$ on a level road. The tension in the coupling is $1000 \ N$. The power used on the mass will be ..... . When the truck moves on an incline of $1 \ m$ rise in $6 \ m$ length,the tension will be ..... .

$A$ body of mass $100 \ gm$ moves with a constant speed along a circular path of radius $r$. What is the work done during one complete revolution?

$A$ $2 \ kg$ block slides on a horizontal surface at a speed of $4 \ m/s$ and strikes an uncompressed spring. The kinetic friction force is $15 \ N$ and the spring constant is $10,000 \ N/m$. By how many $cm$ will the spring be compressed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module