Explanation:
It is given that,
The mass of bob, m = 77 kg
Length of the string, L = 10 m
Angle made by the string with the vertical, [tex]\theta=3^{\circ}[/tex]
(a) Let T is the force exerted by the string on the pendulum. At equilibrium,
[tex]T\ cos\theta=mg[/tex]
[tex]T=\dfrac{mg}{cos\theta}[/tex]
[tex]T=\dfrac{77\times 9.8}{cos(3)}[/tex]
T = 755.63 N
The horizontal component of the force is given by,
[tex]T_H=T\ sin\theta[/tex]
[tex]T_H=755.63\ sin(3)=39.54\ N[/tex]
The vertical component of the force is given by,
[tex]T_V=T\ sin\theta=mg[/tex]
[tex]T_V=754.59\ N[/tex]
(b) Let a is the radial acceleration of the bob. It can be calculated as :
[tex]a=\dfrac{T_H}{m}[/tex]
[tex]a=\dfrac{39.54\ N}{77\ kg}[/tex]
[tex]a=0.51\ m/s^2[/tex]
Hence, this is the required solution.
