question_answer

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 10m starting from rest is (Taking: \[g=10\,Nk{{g}^{-1}}\])

A)  \[0.5\] s                                   

B)  1 s

C)  \[\sqrt{\frac{2}{3}}\] s                          

D)  2 s 

Correct Answer: B

Solution :

Tension in the string \[T-mg\,=30\times 10\,=300\,N\] 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 ms~2. Given, s = 10m and    u = 0 \[10=\frac{1}{2}\,(20)\,{{t}^{2}}\Rightarrow \,t=1\,s\]