Answer:
T=Lnsin
Please check the attached
Explanation:
The torque can simply be calculated by multiplying the length of the rod by the perpendicular force n as shown in the attached figure.
Note that sin90=1
T=Lsin
(nsin90)
T=Lsin
xn
T=Lnsin
Explanation :
It is given that,
Diameter of the coil, d = 20 cm = 0.2 m
Radius of the coil, r = 0.1 m
Number of turns, N = 3000
Induced EMF, 
Magnitude of Earth's field, 
We need to find the angular frequency with which it is rotated. The induced emf due to rotation is given by :




So, the angular frequency with which the loop is rotated is 159.15 rad/s. Hence, this is the required solution.
Answer:
There is no change, unless your mass is somehow at the quantum level, at which the concept of half-life breaks down.
Half life is a property of the specific radioactive isotope...NOT of the initial sample's mass.