Answer:
Explanation:
Expression for time period of a pendulum is as follows
T = 
l is length of pendulum from centre of bob and g is acceleration due to gravity
Given
Time period T = 1.583
g = 9.846
Substituting the values
1.583 = 
l = 
l = .6244 m
= 62.44 cm
Length of rod = length of pendulum - radius of bob
= 62.44 - 13.62
= 48.82 cm
= .488 m
Answer:
The charge on each plate is 0.0048 nC
Explanation:
for the distance between the plates d and given the area of plates, A, and ε = 8.85×10^-12 C^2/N.m^2, the capacitance of the plates is given by:
C = (A×ε)/d
=[(0.2304×10^-2)(0.2304×10^-2)×(8.85×10^-12))/(0.5974×10^-3)
= 7.86×10^-14 F
then if the plates are connected to a battery of voltage V = 61 V, the charge on the plates is given by:
q = C×V
= (7.86×10^-14)×(61)
= 4.80×10^-14 C
≈ 0.0048 nC
Therefore, the charge on each plate is 0.0048 nC.
Explanation:
It is given that,
Magnitude of charge, 
It moves in northeast direction with a speed of 5 m/s, 25 degrees East of a magnetic field.
Magnetic field, 
Velocity, 
![v=[(4.53)i+(2.11)j]\ m/s](https://tex.z-dn.net/?f=v%3D%5B%284.53%29i%2B%282.11%29j%5D%5C%20m%2Fs)
We need to find the magnitude of force on the charge. Magnetic force is given by :

![F=15\times 10^{-6}[(4.53i+2.11j)\times 0.08\ j]](https://tex.z-dn.net/?f=F%3D15%5Ctimes%2010%5E%7B-6%7D%5B%284.53i%2B2.11j%29%5Ctimes%200.08%5C%20j%5D)
<em>Since</em>, 
![F=15\times 10^{-6}[(4.53i)\times (0.08)\ j]](https://tex.z-dn.net/?f=F%3D15%5Ctimes%2010%5E%7B-6%7D%5B%284.53i%29%5Ctimes%20%280.08%29%5C%20j%5D)


So, the force acting on the charge is
and is moving in positive z axis. Hence, this is the required solution.
300/8 = 37.5
37.5 x 12 = 450
New temp. = 450 K
Hope this helps!