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When a body moves with velocity `V_1` for first half of the journey and `V_2` for remaining half of the journey, its average velocity is given by `2/V_"av"=1/V_1+1/V_2` . If `V_1` and `V_2` are `(15pm0.5)` m/s and `(30pm0.1)` m/s, find the average velocity within error limits. |
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Answer» It is given that `V_"av"=(2V_1V_2)/(V_1+V_2)` First, we shall calculate `V_"av"` `V_"av"=(2xx15xx30)/(15+30)`=20 m/s Now, we shall calculate error in `V_"av"` `2/V_"av"=1/V_1+1/V_2 ` `(2dV_"av")/V_a^2=(dV_1)/V_1^2+(dV_2)/V_2` or `(2dV_"av")/400=0.5/225+0.1/900` `dV_a=0.46` `therefore V_"av"=(20pm0.4)`. |
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