Question

Three pendulums A, B and C have frequency 0.5 Hz,
0.05 Hz and 0.005 Hz respectively. The number of
oscillations completed by pendulum A and C in a
time period equal to time taken by pendulum B to
complete 200 oscillations are respectively
(1) 2000, 20
(2) 5000, 50
(3) 50, 5000 (4) 20, 2000​

Answer 1

Answer:

Option (1) 2000, 20

Step-by-step explanation:

Frequency of pendulum B = 0.05 Hz

Therefore, time period of pendulum B

$=\frac{1}{0.05}$ seconds

$=20$ seconds

i.e. in 20 seconds, pendulum B completes 1 oscillation

Therefore, it will complete 200 oscillations in 20 × 200 = 4000 seconds

Frequency of pendulum A = 0.5 Hz

Time period of pendulum A = 1/0.5 = 2 seconds

Thus in 4000 seconds, the oscillations completed by pendulum A

$=\frac{4000}{2}$

$=2000$

Frequency of pendulum C = 0.005 Hz

Time period of pendulum C = 1/0.005 = 200 seconds

Oscillations by pendulum C in 4000 seconds

$=\frac{4000}{200}$

$=20$

Hope this helps.

Answer 2

Answer:

Option 1 is the right answer 2000,20

Explanation:

Frequencies of Pendulums A,B  and C are

F(a)=0.5      Hz                   Number of Oscillations of Pendulum A=x=?

F(b)=0.05   Hz          &       Number of Oscillations=200

F(c)=0.005 Hz                     Number of Oscillations of Pendulum B=y=?

F=1/T or T=1/F

we find first T(a),T(b) and T(c) of all frequencies

T(a)=1/0.5=2s

T(b)=1/0.05=20s

T(c)=1/0.005=200s

We apply the Ratio Method

                         Time Period                                   Number of Oscillations

Pendulum(B)         20s                                                       200

Pendulum(A)          2s                                                          x

             we are moving from Pendulum B to A  So the time period of Pendulum B is 20 s  then Oscillations are 200 when time becomes 2s then it is understood that oscillations becomes less.

20/2=200/x

Rearranging

x/200=2/20

x=(2/20)*200=(1/10)*200=20 oscillations

Now for Pendulum C We want to find Number of Oscillations

We apply the Ratio Method

                         Time Period                                   Number of Oscillations

Pendulum(B)         20s                                                       200

Pendulum(C)          200s                                                       y

We are moving From pendulum B to C.When time period Increases from 20s to 200s then the Number of Oscillation is increased.So

20/200=200/y

Rearranging

y/200=200/20

y=10*200=2000 Oscillations

So the right answer is 20,2000