question_answer

A wooden block of mass m & density p is tied to a string. The other end of the string is fixed to the bottom of the tank. The tank is filled with a liquid of density \[\sigma .\] For this situation mark the INCORRECT statement(s)

A)  lf\[\sigma <\rho \] the string will slack and block sinks

B)  If \[\sigma <\rho \] the string is taut

C)  if \[\sigma >\rho \] the string is taut

D)  If \[\sigma >\rho \]the string is taut and tension in string is\[\frac{\sigma -\rho }{\rho }\times mg\]

Correct Answer: B

Solution :

If \[\sigma <\rho \]the gravitational force is greater then buoyancy force and hence string slacks & block sink When \[\sigma >\rho \]the FBD of block is as shown in figure \[{{F}_{b}}=\frac{m}{\rho }\sigma g=mg+T\] \[\Rightarrow \]\[T=mg\left( \frac{\sigma -\rho }{\rho } \right)\]