Final answer:
Using conservation of mechanical energy, the angle of displacement from the vertical when the bob is at the lowest point is 45 degrees. Option B is correct.
Step-by-step explanation:
Using conservation of mechanical energy, we can find the speed of the bob at the lowest point. When the bob is at its highest point (released from rest), it possesses only potential energy, which can be calculated using the formula PE = mgh, where m is the mass of the bob, g is acceleration due to gravity, and h is the height of the bob above the lowest point.
At the lowest point, all of the potential energy is converted to kinetic energy, given by KE = 1/2 * mv^2, where v is the velocity of the bob. Equating these two energies, we have:
mgh = 1/2 * mv^2
Canceling out m and solving for v, we get:
v = √(2gh)
Substituting g with the acceleration due to gravity, we have:
v = √(2gL)
where L is the length of the string. Since the given velocity is v=√gl, we have:
√(gl) = √(2gL)
Canceling out √g and solving for L, we get:
L = √2l
Therefore, when the bob is at the lowest point, the string makes an angle of 45 degrees with the vertical, which is option (b).