Question

A 10Kg stone is suspended with a rope of breaking strength 30 kg wt.the minimum time in which the stone can be raised through a height 15 m starting from rest is

Answer 1

mass of stone = 10kg
breaking strength = 30kg wt = 30×g = 30g N (g=acceleration due to gravity)

let the maximum acceleration allowed = a
So breaking strength = mg+ma
⇒ 30g = 10g + 10a
⇒ 30g - 10g = 10a
⇒ 10a = 20g
⇒ a = 20g/10 = 2g
⇒ a = 2×10 = 20m/s²

so maximum acceleration allowed = 20m/s²
h = 15m
u = 0
let the time taken = t

h = ut + 0.5at²
⇒ 15 = 0 + 0.5×20×t²
⇒ 15 = 10t²
⇒ t² = 15/10 = 1.5
⇒ t = √1.5 = 1.22s

So minimum time is 1.22s.

Answer 2

Answer:

30=300N

a=f/m

300/10= 30m/s

30=g+a

a=20

s=ut+1/2at^2

15=0+1/2 20×t^2

15=10t^2

1.5=t^2

t=1.2