A horizontal metallic rod of mass m and length l is supported by two vertical identical springs of spring constant, K each and natural length l0 . A current i is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is:

Question

A horizontal metallic rod of mass m and length l is supported by two vertical identical springs of spring constant, K each and natural length l0 . A current i is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-mkksaijwi3wr.png" /> (A) l0+(i l B - m g/K) (B) l0+( textitilB - textitmg/2 K) (C) l0+(m g - i l B/2 K) (D) l0+(m g - i l B/K)

Tardigrade Admin · Accepted Answer

The force on the rod due to the magnetic field and gravity is

i lB - m g (u pw a r d s)

Hence the extension in the springs is

\frac{i lB - m g}{2 k}

(N o t e

that effective spring constant is 2k)
Therefore the length of the spring is

l_{0} + \frac{i lB - m g}{2 k}

Q. A horizontal metallic rod of mass $m$ and length $l$ is supported by two vertical identical springs of spring constant, $K$ each and natural length $l_{0}$ . A current $i$ is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is:

$l_{0} + \frac{i lB - m g}{K}$

$l_{0} + \frac{ilB - mg}{2 K}$

$l_{0} + \frac{m g - i lB}{2 K}$

$l_{0} + \frac{m g - i lB}{K}$

The force on the rod due to the magnetic field and gravity is
$i lB - m g (u pw a r d s)$
Hence the extension in the springs is $\frac{i lB - m g}{2 k}$
$(N o t e$ that effective spring constant is 2k)
Therefore the length of the spring is $l_{0} + \frac{i lB - m g}{2 k}$

Q. A horizontal metallic rod of mass m and length l is supported by two vertical identical springs of spring constant, K each and natural length l0​ . A current i is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is:

l0​+KilB−mg​

l0​+2KilB−mg​

l0​+2Kmg−ilB​

l0​+Kmg−ilB​