A pendulum of length 1 ๐ is releasedfrom ๐ = 60ยฐ. The rate of change ofspeed of the bob at ๐ = 30ยฐ is (๐ =10 ๐๐ โ2).(a) 10 ๐๐ โ2(b) 7.5 ๐๐ โ2(c) 5 ๐๐ โ2(d) 5โ3๐๐ โ2
Question
A pendulum of length 1 ๐ is releasedfrom ๐ = 60ยฐ. The rate of change ofspeed of the bob at ๐ = 30ยฐ is (๐ =10 ๐๐ โ2).(a) 10 ๐๐ โ2(b) 7.5 ๐๐ โ2(c) 5 ๐๐ โ2(d) 5โ3๐๐ โ2
Solution
The rate of change of speed of the bob at ๐ = 30ยฐ can be calculated using the formula for the acceleration of a pendulum, which is a = g * cos(๐).
Step 1: Convert the angle ๐ from degrees to radians. In this case, ๐ = 30ยฐ = ฯ/6 radians.
Step 2: Substitute the values into the formula. a = 10 m/sยฒ * cos(ฯ/6).
Step 3: Calculate the cosine of ฯ/6, which is โ3/2.
Step 4: Multiply the values to get the acceleration. a = 10 m/sยฒ * โ3/2 = 5โ3 m/sยฒ.
So, the rate of change of speed of the bob at ๐ = 30ยฐ is (d) 5โ3 m/sยฒ.
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