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Work, Power and Energy

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Question : 18 of 30
Marks: +1, -0
The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?
Solution:  
Length of pendulum h = 1.5 m
Let m be mass of the bob, then potential energy of the bob at A,
mgh=m×9.8×1.5 Jmgh = m \times 9.8 \times 1.5\,\mathrm{J}
On reaching the lowest point B, the bob will acquire an equal amount ofkinetic energy. But as 5% of energy is lost against the air friction.
Energy converted =95%(mgh)= 95\% (mgh)
If v is the velocity acquired by the bob at the point B, then
K.E.=12mv2=95100mgh\text{K.E.} = \frac{1}{2} m v^{2} = \frac{95}{100} mgh
v=95100×2×ghv = \sqrt{ \frac{95}{100} \times 2 \times g h } =1920×2×9.8×1.5= \sqrt{ \frac{19}{20} \times 2 \times 9.8 \times 1.5 } =5.285 m s−1= 5.285\,\mathrm{m}\,\mathrm{s}^{-1}
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