KVPY Sample Paper KVPY Stream-SX Model Paper-3

A chord attached about an end to a vibrating fork divides it into 6 loops, when its tension is 36 N. The tension at which it will vibrate in 4 loops is:

A) 24 N

B) 36 N

C) 64 N

D) 81 N

Correct Answer: D

Solution :

For waves along a string: \[\upsilon \,\alpha \,\sqrt{T}\]

\[\Rightarrow \] \[\lambda \,\alpha \,\sqrt{T}\]

Now, for 6 loops: \[3{{\lambda }_{1}}=L\] \[\Rightarrow \] \[{{\lambda }_{1}}=L/3\]

& for 4 loops: \[2{{\lambda }_{2}}=L\]\[\Rightarrow \] \[{{\lambda }_{2}}=L/2\]

\[\Rightarrow \] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{1}}}=\frac{2}{3}\]

\[\Rightarrow \] \[{{T}_{2}}=\frac{9}{4}\times {{T}_{1}}=\frac{9}{4}\times 36\]

\[\Rightarrow \] 81 N.