Answer:
work done is -2.8 × 10⁻⁶ J
Explanation:
Given the data in the question;
mass of the pendulum m = 6 kg
Length of core = 1.7 m
Now, case1, mass is pulled aside a small distance of 7.6 cm and released from rest. so let θ₁ be the angle made by mass with vertical axis.
so, θ₁ = ( 7.6 × 10⁻² m / 1.7 m ) = 0.045 rad
In case2, mass is pulled aside a small distance of 8 cm and released from rest. so let θ₁ be the angle made by mass with vertical axis.
so, θ₂ = ( 8 × 10⁻² m / 1.7 m ) = 0.047 rad.
Now, the required work done will be;
![W = \int\limits^{\theta_2} _{\theta_1} {r} \, d\theta](https://tex.z-dn.net/?f=W%20%3D%20%5Cint%5Climits%5E%7B%5Ctheta_2%7D%20_%7B%5Ctheta_1%7D%20%7Br%7D%20%5C%2C%20d%5Ctheta)
![W = \int\limits^{\theta_2} _{\theta_1} {-mgl sin\theta } \, d\theta](https://tex.z-dn.net/?f=W%20%3D%20%5Cint%5Climits%5E%7B%5Ctheta_2%7D%20_%7B%5Ctheta_1%7D%20%7B-mgl%20sin%5Ctheta%20%7D%20%5C%2C%20d%5Ctheta)
![W = -mgl \int\limits^{0.047 } _{0.045 } {sin\theta } \, d\theta](https://tex.z-dn.net/?f=W%20%3D%20-mgl%20%20%5Cint%5Climits%5E%7B0.047%20%7D%20_%7B0.045%20%7D%20%7Bsin%5Ctheta%20%7D%20%5C%2C%20d%5Ctheta)
W =
-cosθ ![]^{0.047}_{0.045 }](https://tex.z-dn.net/?f=%5D%5E%7B0.047%7D_%7B0.045%20%7D)
W = 6 × 9.8 × 1.7 × [ cos( 0.047 ) - cos( 0.045 ) ]
W = 6 × 9.8 × 1.7 × [ -2.8 × 10⁻⁸ ]
W = -2.8 × 10⁻⁶ J
Therefore, work done is -2.8 × 10⁻⁶ J