A 10 kg 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 10 m starting from rest is (Taking g = 10 m/s2)

Question

A 10 kg 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 10 m starting from rest is (Taking g = 10 m/s2) (A) 0.5 s (B) 1.0 texts (C) √(2/3) text s (D) 2.0 texts

Tardigrade Admin · Accepted Answer

Maximum tension in the string T = mg
= 30 x 10
= 300 N

T - mg = ma
From the figure
300 - 10 x 10 = 10a

∴

a = 20 m s^-2
Thus, the maximum acceleration with which the stone can be raised is 20 m s^-2.
Given, s = 10 m
and u = 0

∴

10 = \frac{1}{2} (20) (t)^{2}

\Rightarrow

t = 1 s

Q. A 10 kg 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 10 m starting from rest is

(Taking g = 10 m/s²)

$0.5 s$

$1.0 s$

$\frac{2}{3} s$

$2.0 s$

Maximum tension in the string T = mg
= 30 x 10
= 300 N

T - mg = ma
From the figure
300 - 10 x 10 = 10a
$∴$ a = 20 m s^-2
Thus, the maximum acceleration with which the stone can be raised is 20 m s^-2.
Given, s = 10 m
and u = 0
$∴$ $10 = \frac{1}{2} (20) (t)^{2}$
$\Rightarrow$ t = 1 s

Q. A 10 kg 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 10 m starting from rest is (Taking g = 10 m/s2)

0.5s

1.0s

32​​ s

2.0s