| The tension in a string holding a solid block below the surface of a liquid of density greater than that of solid as shown in figure is Ty, when the system is at rest. Tension in the string if the system has upward acceleration 'a' will be: |
 |
A) \[{{T}_{0}}(a+g)\]
B) \[{{T}_{0}}\left\{ 1+\frac{a}{g} \right\}\]
C) \[{{T}_{0}}\]
D) \[<{{T}_{0}}\]
Correct Answer: B
Solution :
| tension in the string \[{{T}_{0}}={{F}_{b}}-mg\] | |
| \[=V\rho g-mg\] | |
| \[=\frac{m}{{{\rho }_{b}}}pg-mg\] | |
| \[=mg\left( \frac{\rho }{{{\rho }_{b}}}-1 \right)\] | ..(i) |
| When accelerated upward, | |
| \[T=m(g+a)\left( \frac{\rho }{{{\rho }_{b}}}-1 \right)\] | ..(ii) |
| Dividing (ii)/(i) we get | |
| \[T={{T}_{0}}\frac{(g+a)}{g}={{T}_{0}}\left\{ 1+\left( \frac{a}{g} \right) \right\}\] | |
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