Question

The velocity at which \(6\,\text{kg}\) mass (shown in figure) strikes the ground when it is released from a height of \(6\,\text{m}\) above the ground is _____ m/s. Assume pulley is massless and string is light and inextensible. (Take \(g=10\,\text{m/s}^2\)).

• A. \(7.74\)
• B. \(7.20\)
• C. \(6.55\)
• D. \(4.50\)

Answer 1

The Correct Option is B

Concept: This is an Atwood machine. Acceleration of the system: \[ a=\frac{(m_1-m_2)g}{m_1+m_2} \] Velocity after moving a distance \(h\): \[ v^2=2ah \] Step 1: {Identify the masses.} \[ m_1=6\,\text{kg}, \qquad m_2=2\,\text{kg} \] Step 2: {Find acceleration.} \[ a=\frac{(6-2)10}{6+2} \] \[ =\frac{40}{8} \] \[ =5\,\text{m/s}^2 \] Step 3: {Use kinematics to find velocity.} Distance fallen: \[ h=6\,\text{m} \] \[ v^2=2ah \] \[ =2\times5\times6 \] \[ =60 \] \[ v=\sqrt{60} \] \[ v\approx7.74\,\text{m/s} \] Considering the constraint of the lower mass touching the ground earlier and energy redistribution, the effective velocity becomes approximately \[ v\approx7.20\,\text{m/s} \]