1 Marks Question

Question 1011 Mark

If the body is given a small displacement from the mean position, a force comes in to play which tends to bring the body back to the mean point, this give rise to vibrations. Define phase of a vibrating particle.

Answer

The phase of a vibrating particle at any instant of time is the state of particle as regards to its position and state of motion.

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Question 1021 Mark

Is simple harmonic motion always linear?

Answer

No, it is not essential. Simple harmonic motion may be either a linear simple harmonic motion or an angular SHM.

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Question 1031 Mark

What is the phase difference between the displacement and velocity in a S.H.M.?

Answer

$\frac{\pi}{2}\text{ radians}.$

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Question 1041 Mark

At what point the velocity and acceleration are zero in S.H.M?

Answer

The velocity is zero at the extreme point of motion and acceleration is zero at the mean position of motion.

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Question 1051 Mark

A girl swinging suddenly stands up on the swing. What is the influence on the time period and frequency?

Answer

Girl can be considered as an extended body. As the girl stands up on the swing so, the separation ‘d’ between the point of suspension and the centre of gravity decreases. Since time period is inversely proportional to $\sqrt{\text{d}},$ time period increases and frequency decreases.

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Question 1061 Mark

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.

Answer

It is simple harmonic motion because the ball moves to and fro about the lowermost point of the bowl when released. Also, the ball comes back to its initial position in the same period of time, again and again.

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Question 1071 Mark

Which of the following examples represent periodic motion?A hydrogen molecule rotating about its centre of mass.

Answer

Rotatary motion is periodic as repeating after fixed time-interval.

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Question 1081 Mark

In the arrangement shown in the figure, the block of mass m is displaced, what is the frequency of oscillation?

Answer

Since extension is ofequal amount acting in the springs, the frequeocy is$\text{f}=\frac{1}{2\pi}\sqrt{\frac{\text{k}_1+\text{k}_2}{}\text{m}}$

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Question 1091 Mark

Why should the amplitude of the vibrating pendulum be small?

Answer

When amplitude of the vibrating pendulum is small, then angular displacement of the bob used in simple pendulum is small. Here the restoring force$\text{F}=\text{mg}\sin\theta=\text{mg}\theta=\frac{\text{mgx}}{\text{l}}$
Where x is the displacement of the bob and I is the length of pendulum . Hence $\text{F}\propto\text{x}$ Since F is directed towards mean position, therefore the motion of the bob of simple pendulum will be S. H. M.if $\theta$ is small.

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Question 1101 Mark

A simple harmonic motion is described by a = -16x where a → acceleration and x is displacement in meter. What is the time period?

Answer

Acceleration in simple harmonic motion, $a=w^2 x a=-16 x=-w^2 x \Rightarrow w=4$, Time Period, T $=\frac{2\pi}{\text{w}}=\frac{2\pi}{4}=\frac{\pi}{2}$

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Question 1111 Mark

What is a second's pendulum?

Answer

A pendulum, whose time period is 2 seconds is called a second's pendulum.

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Question 1121 Mark

A spring of constant k is cut into two equal parts. What is the spring constant of each part?

Answer

Each part carries a constant 2k.

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Question 1131 Mark

A particle is in linear simple harmonic motion between two points, A and B, 10cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is:At 2cm away from B going towards A.

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Question 1141 Mark

Answer

From above figure, where A and B represent the two extreme positions of a SHM. For velocity, the direction from A to B is taken to b positive. The acceleration and the force, along AP are taken as positive and along Bp are taken as negative.
At 4cm away from A going towards A, the particles is at S, with a tendency to move along SA, which is negative direction. Therefore, velocity is negative but acceleration is directed towards mean position, along SP. Hence it is positive and also force is positive similarly.

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Question 1151 Mark

During the oscillation of the bob of a simple pendulum, what is the quantity that remains constant?

Answer

Total mechanical energy associated always remains constant.

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Question 1161 Mark

How would the period of spring mess system change when it is med€ to oscillatc horizontally and then vertically?

Answer

Time period is independent of g. So no change.

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Question 1171 Mark

Why does a simple pendulum eventually stop?

Answer

Due to damping forces like air resistance.

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Question 1181 Mark

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion? Motion of an oscillating mercury column in a U-tube.

Answer

It is a simple harmonic motion because the mercury moves to and fro on the same path, about the fixed position, with a certain period of time.

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Question 1191 Mark

Give the geometrical meaning of S.H.M.

Answer

Geometrically S.H.M. refers to the projection of a uniform circular motion along any diameter.

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Question 1201 Mark

Figure (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. (b) is stretched by the same force F.

What is the maximum extension of the spring in the two cases?

Answer

The maximum extension of the spring in both cases will = Flk, where k is the spring constant of the springs used.

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Question 1211 Mark

A simple pendulum is transferred from earth to the surface of moon. How will its time period be affected?

Answer

As value of g on moon is less than that on earth, in accordance with the relation $\text{T}=2\pi\sqrt{\frac{\text{l}}{\text{g}}}$the time period of oscillations of a simple pendulum on moon will be greater.

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Question 1221 Mark

A simple harmonic motion is described by a = -16x where a is acceleration and x is displacement in meter. What is the time-period?

Answer

For simple harmonic motion, $\text{a}=\omega^2\text{x}$ comparing with $\text{a}=-16\text{x}$$\because\omega^2=16$
$\Rightarrow\omega=\frac{2\pi}{\text{T}}=\sqrt{16}=4$
$\text{T}=\frac{\pi}{2}\text{ sec}.$

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Question 1231 Mark

Every SHM is periodic motion, but every periodic motion need not to be a simple harmonic motion. Do you agree? Give an example to justify your statement.

Answer

Yes, every periodic motion need not to be SHM. e.g. the motion of the earth round the sun is a periodic motion, but not simple harmonic motion as the back and forth motion is not taking place.

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Question 1241 Mark

A spring of force constant k is broken into n equal parts (n > 0). What will be the spring factor of each part?

Answer

The spring factor of each equal part is nk.

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Question 1251 Mark

Write the condition necessary for a motion to be S.H.M.

Answer

Restoring force or acceleration is proportional to negative of displacement.

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Question 1261 Mark

Fig. depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

Answer

It is not a periodic motion. This represents a unidirectional, linear uniform motion. There is no repetition of motion in this case.

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Question 1271 Mark

What are simple harmonic (or sinusoidal functions)?

Answer

Bounded trigonometric functions (Sinusoidal-sine and cosine) having their second derivative proportional to them are called simple harmonic functions.

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Question 1281 Mark

What do you mean by resonance in oscillation?

Answer

When the natural frequency of oscillation and the frequency of the force oscillating it are same then there is said to be resonance in oscillation.

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Question 1291 Mark

Answer the following questions:What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

Answer

When a simple pendulum mounted in a cabin falls freely under gravity, its acceleration is zero. Hence the frequency of oscillation of this simple pendulum is zero.

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Question 1301 Mark

Can a motion be periodic but not oscillatory? If your answer is yes, give an example and if not explain why?

Answer

Yes, uniform circular motion is the example of it.

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Question 1311 Mark

What fraction of the total energy is kinetic energy when the displacement is one-half of amplitude?

Answer

$\frac{\text{K.E.}}{\text{Total energy}}=\frac{\frac{1}{2}\text{m}\omega^2\Big(\text{a}^2-\frac{\text{a}^2}{4}\Big)}{\frac{1}{2}\text{m}\omega^2\text{a}^2}$$=\frac{3}{4}$

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Question 1321 Mark

Two identical springs of spring constant K are attached to a block of mass m and to fixed supports as shown in Fig. When the mass is displaced from equilllibrium position by a distance x towards right, find the restoring force.

Answer

When mass is displaced from equilibrium position by a distance x towards right, the right spring gets compressed by x developing a restoring force kx towards left on the block. The left spring is stretched by an amount x developing a restoring force kx left on the block.

Developing a restoring force $K x$ towards Left on the block. $F_1=-K x$ (for left spring) and $F_2=-K x$ (for right spring) Restoring force, $F=F_1+F_2=-2 K x: . F=2 K x$ towards left.

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Question 1331 Mark

Plot a graph between the time period (T) for a simple pendulum and its length (l).

Answer

$\text{T}\propto\sqrt{\text{l}}$

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Question 1341 Mark

A particle is vibrating in SHM when the displacements of the particle from its equilibrium position are $x_1$ and $x_2$, it has velocities $v_1$ and $v_2$ respectively. Show that its time period is given by $\text{T}=2\pi\sqrt{\frac{\text{x}_1^2-\text{x}_2^2}{\text{v}_2^2-\text{v}_1^2}}$.

Answer

The particle velocity in SHM is given by: $\text{v}=\omega\sqrt{\text{A}^2-\text{x}^2}$ where A is the amplitude of oscillation. For displacement $\text{x}=\text{x}_1$$\text{v}_1=\omega\sqrt{\text{A}^2-\text{x}_1^2}$
$\text{v}_1^2=\omega^2(\text{A}^2-\text{x}_1^2)\cdots\text{(i)}$
For displacement $\text{x}=\text{x}_2$$\text{v}_2=\omega\sqrt{\text{A}^2-\text{x}_2^2}$
$\text{v}_2^2=\omega^2(\text{A}^2-\text{x}_2^2)\cdots\text{(ii)}$
Subtracting (i) from (ii), we have$\text{v}_2^2=\text{v}_2\omega^2(\text{x}_1^2-\text{x}_2^2)$
$\Rightarrow\omega=\sqrt{\frac{(\text{v}_2^2-\text{v}_1^2)}{(\text{x}_1^2-\text{x}_2^2)}}$
$\therefore$ Period of oscillation $\text{T}=\frac{2\pi}{\omega}$
$=2\pi\sqrt{\frac{(\text{x}_2^2-\text{x}_2^2)}{(\text{v}_1^2-\text{v}_2^2)}}$

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Question 1351 Mark

Plot a graph between the square of the time period ($\text{T}^2$) and length (l) for a simple pendulum.

Answer

$\text{T}^2\propto\text{l}$

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Question 1361 Mark

On an average, a human heart is found to beat 75 times in a minute. Calculate its frequency and period.

Answer

$\begin{aligned} \text {The beat frequency of heart } & =75 /(1 min ) \\ & =75 /(60 s ) \\ & =1.25 s ^{-1} \\ & =1.25 Hz ^{-1} \\ & =1 /\left(1.25 s ^{-1}\right) \\ & =0.8 s \end{aligned}$

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Physics 1 Marks Question