A simple pendulum, consisting of a mass on a string of length L, is undergoing small oscillations with amplitude A.
1. The mass is increased by a factor of four. What is true about the period?
Choose the best answer.
a. The period is halved.
b. The period increases by a factor of four.
c. The period remains unchanged.
d. The period doubles.
e. The period decreases by a factor of four.

A. Period is halved

Explanation:

The period of a pendulum swing, T, is given in terms of mass as:

where I = moment of inertia

m = mass of the pendulum

g = acceleration due to gravity

h = Length of string

If the mass is increased by a factor of 4, that means:

M = 4m

(M = new mass)

The new period of the pendulum, , will now be:

Hence, the period is halved.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards