| A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant \[0.5N{{m}^{-1}}.\](see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance \[10\,\Omega \] and air drag negligible, N will be close to: |
 |
A) 50000
B) 1000
C) 10000
D) 5000
Correct Answer: D
Solution :
| \[-KX-\frac{v{{\ell }^{2}}{{B}^{2}}}{R}=ma\] |
| \[A={{A}_{0}}{{e}^{-bt/2m}}\] |
| \[t=\frac{2mR}{{{B}^{2}}{{\ell }^{2}}}\]\[=\frac{2(50\times {{10}^{-3}})(10)}{{{(0.1)}^{2}}{{(0.1)}^{2}}}={{10}^{4}}\] |
| \[t=2\pi \sqrt{m/K}=2\,\sec \]\[\Rightarrow \]\[f=0.5\text{ }Hz\] |
| \[N=5000.\] |
You need to login to perform this action.
You will be redirected in
3 sec
