A book with printing error contains four different formulae for d… - Vidyadip

Question

A book with printing error contains four different formulae for displacement. Choose the correct formula/formulae (a) $y=a \sin \frac{2 \pi}{ T } t$
(b) $y=a \sin v t$
(c) $y=\frac{a}{ T } \sin \left(\frac{t}{a}\right)$
(d) $y=\frac{a}{T}\left(\sin \frac{2 \pi}{ T } t+\cos \frac{2 \pi}{ T } t\right)$

✓

Answer

The arguments of sine and cosine function must be dimensionless so (a) is the probable correct formulae. Since
(a) $y=a \sin \left(\frac{2 \pi}{ T } t\right), \therefore\left[\frac{2 \pi t}{ T }\right]=\left[ T ^0\right]$ is dimensionless.
(b) $y=a \sin v t, \quad \because[v t]=[ L ]$ is dimensional so this equation is incorrect.
(c) $y=\frac{a}{t} \sin \left(\frac{t}{a}\right), \because\left[\frac{t}{a}\right]$ is dimensional so this is incorrect.
(d) $y=\frac{a}{t}\left(\sin \frac{2 \pi}{ T } t+\cos \frac{2 \pi t}{ T }\right):$ Though $\frac{2 \pi t}{ T }$ dimensionless $\frac{a}{ T }$ does not have dimensions of displacement so this is also incorrect.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[ 2 Marks Questions ]" from Nature of Physical World and Measurement→Nature of Physical World and Measurement — all question types→Physics STD 11 question papers→Tamilnadu Board STD 11 question papers→Tamilnadu Board question paper generator→

Similar questions

Two simple harmonic motions are represented by the equations: $x_1=5 \sin \left(2 \pi t+\frac{\pi}{4}\right) ; x^2=5 \sqrt{2}(\sin 2 \pi t+\cos 2 \pi t)$What is the ratio of their amplitudes?

What is the angle between $(\overrightarrow{ A }+\overrightarrow{ A })$ and $(\overrightarrow{ A }-\overrightarrow{ A })$ ?

A calorie is a unit of heat or energy and it equals $4.2 J$ where $1 J =1 kg m ^2 s ^{-2}$. Suppose we employ a system of units in which unit of mass is $\alpha kg$, unit of length is $\beta m$, unit of time $\gamma s$. What will be magnitude of calorie in terms of this new system.

What is Boltzmann’s constant? Give its value.

What is circular motion? Give example.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2s. Find the acceleration and velocity of the body when the displacement is 5 cm.

A train is moving on a straight track with acceleration a. A passenger drops a stone. What is the acceleration of stone with respect to passenger?

An insulated container containing monoatomic gas of molar mass m is moving with a velocity v0. If the container is suddenly stopped. Find the change in temperature.

Two cars moving in opposite directions approach each other with speed of $22 ms ^{-1}$ and $16.5 ms ^{-}$ ${ }^1$ respectively. The driver of the first car blows a horn having a frequency $400 Hz$. To find the frequency heard by the driver of the second car.

A solid floats in liquid A with half its volume immersed and in liquid B with $\frac{2}{3}$ of its volume immersed. The densities of the liquids $A$ and $B$ are in the ratio.