If the length of the pendulum is decreased by 2 percent. . .

Question : If the length of the pendulum is decreased by 2 percent, then time period per day :

(A) gain by 864 s

(B) loss by 864 s

(D) loss by 846 s

Doubt by Girisha

Solution :

ΔL/L=-2%

We know,

Clearly
T∝√L
so
ΔT/T = ½ΔL/L

Note : Whenever small change / percentage change / error is written in the question, we use this fractrional change formula.

ΔT/T = ½ΔL/L
ΔT/T = ½(-2%)

ΔT/T = -1%

In one day, we have
=24×60×60 seconds
=86400 seconds

Error per day in Time
=-1% of 86400 seconds

=-(1/100)×86400
=-864 seconds

Negative sign time shows that the Time period reduces, it means the clock runs faster hence the the clock gains time.

So, (A) gain by 864 s, would be the correct option.

Note :

Length ↓ → Period ↓ → Clock fast → Gain time

Length ↑ → Period ↑ → Clock slow → Lose time

Similar Questions :

1. If the length of a simple pendulum is increased by 2% then the time period
(A) increases by 1%
(B) decreases by 1%
(C) increases by 2%
(D) decreases by 2%

Ans : (A) increases by 1%

2. If the length of a simple pendulum is decreased by 2 %, find the percentage decrease in its period T, where T=2 π√(l/g).

Ans : 1.005% ≈ 1%

3. If the length of second’s pendulum is decreased by 2%, how many seconds, it will gain per day?
(A) 3927s
(B) 3727s
(C) 3427s
(D) 864s

Ans : (D) 864s

4. Length of second's pendulum is decreased by 1%, then the gain or loss in time per day will be

(A) gain 4.40 s

(B) gain 432 s

(D) loses 44s

Ans : (B) gain 432 s

5. A pendulum clock is calibrated to keep perfect time at 20°C. If the average temperature rises to 30°C during the summer, the clock will:

(A) Run fast and gain time

(B) Run slow and lose time

(D) Keep perfect time regardless of temperature

Ans : (B) Run slow and lose time.

6. In a very cold winter, a pendulum clock is observed to be "running fast." This is because:(A) The density of air increases, providing more buoyancy.
(B) The value of gravity (g) increases in cold weather.
(C) The pendulum rod contracts, decreasing the time period.
(D) The pendulum rod expands, increasing the time period.

Ans : (C) The pendulum rod contracts, decreasing the time period.