A) \[\left[ 1-{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}} \right]\frac{A}{Mg}\]
B) \[\left[ 1-{{\left( \frac{T}{{{T}_{M}}} \right)}^{2}} \right]\frac{A}{Mg}\]
C) \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{A}{Mg}\]
D) \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{Mg}{A}\]
Correct Answer: C
Solution :
[c] As we know, time period, \[T=2\pi \sqrt{\frac{\ell }{g}}\] When additional mass M is added then \[{{T}_{M}}=2\pi \sqrt{\frac{\ell +\Delta \ell }{g}}\] \[{{T}_{\frac{M}{T}}}=\sqrt{\frac{\ell +\Delta \ell }{\ell }}\,\,\,or\,\,\,{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}=\frac{\ell +\Delta \ell }{\ell }\] or, \[{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}=1+\frac{Mg}{Ay}\] \[\left[ \therefore \,\Delta \ell =\frac{Mg\ell }{Ay} \right]\] \[\therefore \,\,\frac{1}{y}=\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{A}{Mg}\]
You need to login to perform this action.
You will be redirected in
3 sec
