The correct option is D 10 cm
Let 2l be the length of the magnet.
The magnetic field due to a long magnet at an axial point is given by
Bax=(μ04π)2Mx(x2−l2)2
∴B10cm=μ04π2M(10)[102−l2]2 .....(1)
Similarly,
B20cm=μ04π2M(20)[(20)2−l2]2 ......(2)
After equations (1)÷(2), we get
B10cmB20cm=(1020)[(20)2−l2]2[(10)2−l2]2
∵B10cmB20cm=12.51
12.51=12×(400−l2100−l2)2
251=(400−l2100−l2)2
±5=400−l2100−l2
±500∓5l2=400−l2
l=±5 or ±5√6
Since, the length of magnet can't be negative.
∴l=5 cm or 5√6 cm
Therefore, the length of the magnet will be 2l=10 cm or 10√6 cm.
Hence, option (D) is correct.