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.

Answer 1

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.