A rectangular plank of mass 'm₁' and height 'a' is on a horizontal surface. On the top of it another rectangular plank of mass 'm₂' and height 'b' is placed. The potential energy of the system is,

Easy

A

$\large ({m_1} + {m_2})\frac{{(a + b)}}{2}g$
B

$\large \left[ {\frac{{{m_1} + {m_2}}}{2}.a + {m_2}\frac{b}{2}} \right]g$
C

$\large \left[ {\left( {\frac{{{m_1}}}{2} + {m_2}} \right)a + {m_2}\frac{b}{2}} \right]g$
D

$\large \left[ {\left( {\frac{{{m_1}}}{2} + {m_2}} \right)a + {m_1}\frac{b}{2}} \right]g$

Solution

P.E= $m_{1} g \frac{a}{2} + m_{2} g (a + \frac{b}{2})$

$\large PE = \left[ {{m_1}\frac{a}{2} + {m_2}\left( {a + \frac{b}{2}} \right)} \right]g$

$\large PE = \left[ {\left( {\frac{{{m_1}}}{2} + {m_2}} \right)a + \frac{{{m_2}b}}{2}} \right]g$

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