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 $g =10 \,N\,kg ^{-1}$ )
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 $g =10 \,N\,kg ^{-1}$ )
Updated On: Jun 14, 2022
- $ 0.5\,s $
- $ 1.0\,s $
- $ \sqrt{\frac{2}{3}}\,s $
- $ 2.0\,s $
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The Correct Option is B
Solution and Explanation
Tension in the string $(T)=m \times g$
$=30 \times 10=300\, N$
$T-M g=M a$
From the figure $300-10 \times 10 a$
$\Rightarrow a=20 ms ^{-2}$
Thus, the maximum acceleration with
which the stone can be raised is $20 ms ^{-2}$
Given, $s=10 m$
and $u=0$
$\therefore 10=\frac{1}{2}(20) t^{2}$
$t=1\,s$
$=30 \times 10=300\, N$
$T-M g=M a$
From the figure $300-10 \times 10 a$
$\Rightarrow a=20 ms ^{-2}$
Thus, the maximum acceleration with
which the stone can be raised is $20 ms ^{-2}$
Given, $s=10 m$
and $u=0$
$\therefore 10=\frac{1}{2}(20) t^{2}$
$t=1\,s$
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Concepts Used:
Tension
A force working along the length of a medium, especially if this force is carried by a flexible medium like cable or rope is called tension. The flexible cords which bear muscle forces to other parts of the body are called tendons.
Net force = 𝐹𝑛𝑒𝑡 = 𝑇−𝑊=0,
where,
T and W are the magnitudes of the tension and weight and their signs indicate a direction, be up-front positive here.
Read More: Tension Formula