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Chapter 3: Problem 73

The time period of ' \(\mathrm{A}\) ' is, \(\mathrm{T}_{1}=\frac{\mathrm{T}}{20}\). The time period of ' \(\mathrm{B}\) ' is, \(\mathrm{T}_{2}=\frac{\mathrm{T}}{30}\) The ratio of time periods of ' \(A\) ' and ' \(B\) ' is \(\frac{T_{1}}{T_{2}}=\frac{\frac{T}{20}}{\frac{T}{30}}=\frac{30}{20}=\frac{3}{2}\) \(T_{1}: T_{2}=3: 2\)

Short Answer

Expert verified
Answer: The ratio of the time periods of A and B is \(3:2\).

Step by step solution

01

Understanding the given information

The time period of A and B is given as \(T_{1}=\frac{T}{20}\) and \(T_{2}=\frac{T}{30}\), where T represents some constant time period.
02

Set up the equation for the ratio

We are asked to find the ratio \(\frac{T_{1}}{T_{2}}\), which can be written as: \(\frac{T_{1}}{T_{2}}=\frac{\frac{T}{20}}{\frac{T}{30}}\)
03

Simplify the equation

To simplify this fraction of fractions, we can multiply the numerator by the reciprocal of the denominator: \(\frac{T_{1}}{T_{2}}=\frac{\frac{T}{20}}{\frac{T}{30}} \times \frac{30}{T}\) Here, the Ts will cancel out, leaving only: \(\frac{30}{20}\)
04

Simplify the fraction

Simplify the fraction \(\frac{30}{20}\) by dividing both the numerator and the denominator by 10: \(\frac{30}{20}=\frac{3}{2}\)
05

Write the ratio

Now, we can rewrite our simplified fraction as a ratio: \(T_{1}: T_{2}=3: 2\) So, the ratio of the time periods of A and B is \(3:2\).

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Most popular questions from this chapter

Fill in the Blanks. \(5 \mathrm{~m} \mathrm{~s}^{-2}\) \(\mathrm{a}=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}=\frac{20-10}{2}=5 \mathrm{~m} \mathrm{~s}^{-2}\)

Fill in the Blanks. length \(\mathrm{T} \alpha \sqrt{\ell}\) Time period of a simple pendulum depends on its length.

(a) Uniform Velocity: When a body moves with uniform speed in a specified direction, it is said to be moving with uniform velocity. Thus, a body moves with uniform velocity when its magnitude as well as its direction remains the same. Example: Aeroplane moving with \(500 \mathrm{~km} \mathrm{~h}^{-1}\) towards east. (b) Variable velocity: When a body moves such that either its magnitude or direction or both change, then it is said to be moving with variable velocity. Example: A car moving on a straight road such that its speed changes from time to time has variable velocity. A car taking turn has variable velocity as its direction changes.

The speed and average speed of the vehicle can be equal if the vehicle moves with uniform speed or constant speed.

Consider a body moving with initial velocity u. Let its velocity change to \(\mathrm{v}\), in time ' \(\mathrm{t}^{\prime}\). Then, the change in velocity is \(=\mathrm{v}-\mathrm{u}\). The change in velocity per unit time \(=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\) By definition, the change in velocity per unit time is acceleration, a. Thus, \(\mathrm{a}=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\) or \(\mathrm{v}-\mathrm{u}=\) at \(\mathrm{v}=\mathrm{u}+\mathrm{at}\)
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