The time period of a simple pendulum is 2 seconds. If its length is increased by 4 times, then its period becomes:

Explanation

The formula for the period of a simple pendulum is: T = 2π √(L/g) Where: T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity. In this case, we have a pendulum with a period of 2 seconds. So, we can substitute these values into the formula: 2 = 2π √(L/g) Now, let's consider the length of the pendulum increased by 4 times. Let's call the new length L'. So, we have: T' = 2π √(L'/g) To compare the periods, we can divide the two equations: T' / T = (2π √(L'/g)) / (2π √(L/g)) Simplifying this equation, we get: T' / T = √(L'/g) / √(L/g) T' / T = √(L') / √L Since the length is increased by 4 times, we can write L' = 4L: T' / T = √(4L) / √L T' / T = 2√L / √L T' / T = 2 Therefore, the period of the pendulum becomes 2 times the original period. Since the original period is 2 seconds, the new period will be 2 * 2 = 4 seconds.