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Question
The total energy E possess by a body of Mass 'm', moving with a velocity 'v' at a height 'h' is given by: E = `(1)/(2) "m" "u"^2 + "mgh"`. Find m, if v = 2, g = 10, h = 5 and E = 104.
Solution
E = `(1)/(2)"m" "u"^2 + "mgh"`
⇒ E = `"m"(1/2 "u"^2 + "gh")`
⇒ m = `"E"/(1/2 "u"^2 + "gh")`
⇒ m = `"E"/(("u"^2 + 2"gh")/(2)`
⇒ m = `(2"E")/("u"^2 + 2"gh")`
Given that v = 2, g = 10, h = 5 and E = 104
⇒ m = `(2(104))/((2)^2 + 2(10)(5)`
⇒ m = `(208)/(4 + 100)`
⇒ m = 2.
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