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A tank is filled up to a height 2H WITH A LIQUID and is placed on a platform of height H from the ground .the distance x from the ground where a small hole is punched to get maximum range R is?
Ans) let the distance be x.then range(R)=2 . [(3H-x).x]^1/2 ......................... [ since t=(2x/g)^1/2 and v={2g(3H-x)}^1/2 ] R^2 = 4.(3Hx-x^2) for R to be max...R^2 should be max.hence differentiating and putting d(R^2)/dx=0.we get 3H-2x=0x=3H/2.
What is the work done to take a particle of mass m from surface of the earth to a height equal to 2R (R=radius of earth )? Ans) Initial PE= - GMm/R Final PE = - GMm/3R
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