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 10 m starting from rest is \[\left( \text{Taking g}=\text{ 1}0\text{ Nk}{{\text{g}}^{-1}} \right)\]

A)  \[0.5\,s\]                           

B)  \[1.0\,s\]

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

D)  \[2.0\,s\]

Correct Answer: B

Solution :

                 Tension  in the  string  \[(T)=m\times g\]                                                                 \[=30\times 10\]                                                                 \[=300\,N\]                                                                 \[T-Mg=Ma\] From the figure \[300-10\times 10a\] \[\Rightarrow \]                                               \[a=20\,\,m{{s}^{-2}}\] Thus, the maximum acceleration with which the stone can be raised is \[a=20\,\,m{{s}^{-2}}\] Given,   \[s=10m\] and        \[u=0\] \[\therefore \]  \[10=\frac{1}{2}(20)\,{{t}^{2}}\]