Explanation:
Since, it is given that one hand completes 3.19 vibrations in 8.46 sec. Therefore, in one second the number of vibrations will be as follows.

= 0.377 vibrations
Hence, frequency (f) = 0.38 Hz
Now, formula to calculate the speed is as follows.
v = 
or,
= 
= 1.57 cm
Thus, we can conclude that the wavelength is 1.57 cm.
Explanation:
The nearest star to the Earth is the red dwarf star Proxima Centauri, at a distance of 4.218 light-years.
Light year is the unit of distance covered by the heavenly bodies. 1 light year is equal to :
So,
We need to convert 4.218 light-years barley corns.
Since, 1 barleycorn = 1/3 inch


So, the nearest star to the Earth is at a distance of
. Hence, this is the required solution.
Answer:
The correct option is (b).
Explanation:
Given that,
Electric field, 
We need to find the magnitude of the force on the electron as a result of the electric field.
We know that, the electric force is given by :

So, the required force on the electron is equal to
.