Complete Question
The complete question is shown on the first uploaded image
Answer:
The uncertainty in inverse frequency is ![\Delta [\frac{1}{w} ]= \frac{3}{2000} \ s](https://tex.z-dn.net/?f=%5CDelta%20%20%5B%5Cfrac%7B1%7D%7Bw%7D%20%5D%3D%20%20%5Cfrac%7B3%7D%7B2000%7D%20%5C%20s)
Explanation:
From the question we are told that
The value of the proportionality constant is 
The strength of the magnetic field is 
The change in this strength of magnetic field is
The magnetic field is given as

Where
is frequency
The uncertainty or error of the field is given as
![\Delta B = \frac{k }{[\frac{1}{w}^]^2 } \Delta [\frac{1}{w} ]](https://tex.z-dn.net/?f=%5CDelta%20%20B%20%20%3D%20%20%5Cfrac%7Bk%20%7D%7B%5B%5Cfrac%7B1%7D%7Bw%7D%5E%5D%5E2%20%7D%20%20%5CDelta%20%5B%5Cfrac%7B1%7D%7Bw%7D%20%5D)
The uncertainty in inverse frequency is given as
![\Delta [\frac{1}{w} ] = \frac{\Delta B}{k [\frac{1}{w^2} ]}](https://tex.z-dn.net/?f=%5CDelta%20%20%5B%5Cfrac%7B1%7D%7Bw%7D%20%5D%20%20%3D%20%5Cfrac%7B%5CDelta%20B%7D%7Bk%20%5B%5Cfrac%7B1%7D%7Bw%5E2%7D%20%5D%7D)
![\Delta [\frac{1}{w} ]= \frac{\Delta B}{k (B)^2 }](https://tex.z-dn.net/?f=%5CDelta%20%20%5B%5Cfrac%7B1%7D%7Bw%7D%20%5D%3D%20%20%5Cfrac%7B%5CDelta%20B%7D%7Bk%20%28B%29%5E2%20%7D)
substituting values
![\Delta [\frac{1}{w} ]= \frac{3}{5 (20)^2 }](https://tex.z-dn.net/?f=%5CDelta%20%20%5B%5Cfrac%7B1%7D%7Bw%7D%20%5D%3D%20%20%5Cfrac%7B3%7D%7B5%20%2820%29%5E2%20%7D)
![\Delta [\frac{1}{w} ]= \frac{3}{2000} \ s](https://tex.z-dn.net/?f=%5CDelta%20%20%5B%5Cfrac%7B1%7D%7Bw%7D%20%5D%3D%20%20%5Cfrac%7B3%7D%7B2000%7D%20%5C%20s)
As we know that Nth harmonic of the string is given by

now here we will have




now from above formula we have


now for first harmonic N = 1

for second harmonic N = 2

for third harmonic N = 3
Answer: (c) 2000 N
Explanation:
Given Data :
▪ Initial velocity = zero ( body is at rest)
▪ Distance travelled = 100m
▪ Final kinetic energy = 200000J
To Find :
▪ Resultant force acting on the car.
Therefore:
W = F × d = ΔK ----------------- eq 1.
where,
W = work done
F = applied force
d = distance
ΔK = change in kinetic energy
Calculation :
→ F × d = Kf - Ki ----------------- eq 2.
Where:
Kf = Final kinetic energy = 200000
Ki = initial kinetic energy = 0
Substituting our values into the formula from equation (2)
→ F × 100 = 200000 - 0
→ F = 200000/100
→ F = 2000N
The atom carbon is the answer