The acceleration of the particle moving with simple harmonic motion is inversely proportional to the displacement of the particle from the mean position.

Which of the following is/are the characteristics of simple harmonic motion (i) The total energy is conserved (ii) The acceleration is directly proportional to the displacement and is directed towards its mean position (iii) The simple harmonic motion cannot be represented using sinusoidal functions (iv) There are a maximum and minimum displacement about the equilibrium point

A

All the options

B

(i), (ii) and (iii)

C

(i), (ii) & (iv)

D

(i), (iii) & (iv) only

Consider the following statements: 1. If x is directly proportional to z and y is directly proportional to z, then (x2 - y2) is directly proportional to z2. 2. If x is inversely proportional to z and y is inversely proportional to z, then (xy) is inversely proportional to z2. Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by (where, r = Amplitude of motion and y = Displacement of the particle from mean position.)

A

$$\omega \sqrt {{{\text{y}}^2} - {{\text{r}}^2}} $$

B

$$\omega \sqrt {{{\text{r}}^2} - {{\text{y}}^2}} $$

C

$${\omega ^2}\sqrt {{{\text{y}}^2} - {{\text{r}}^2}} $$

D

$${\omega ^2}\sqrt {{{\text{r}}^2} - {{\text{y}}^2}} $$

How is the degree of emulsion polymerization related to the monomer concentration, and the rate of radical generation, Ri? , inversely proportional to Ri b) inversely proportional to Ri, directly proportional to . c) directly proportional to Ri, independent of . d) directly proportional to , independent of Ri

A

and the rate of radical generation, Ri? ] directly proportional to , inversely proportional to Ri

B

M

C

M

D

M

Statement: In simple harmonic motion, the velocity is maximum, when the acceleration is minimum. Reason: Displacement and velocity in simple harmonic motion is differ in phase by π/2.

A

Both statement and reason are true and the reason is the correct explanation of the statement

B

Both statement and reason are true but the reason is not the correct explanation of the statement

C

Statement is true, but the reason is false

D

Statement and reason are false

The velocity of a particle moving with simple harmonic motion, at any instant is given by (where $$\omega $$ = Displacement of the particle from mean position)

A

$$\omega \sqrt {{{\text{x}}^2} - {{\text{r}}^2}} $$

B

$$\omega \sqrt {{{\text{r}}^2} - {{\text{x}}^2}} $$

C

$${\omega ^2}\sqrt {{{\text{x}}^2} - {{\text{r}}^2}} $$

D

$${\omega ^2}\sqrt {{{\text{r}}^2} - {{\text{x}}^2}} $$

Every simple harmonic motion is periodic motion, but every periodic motion need not be simple harmonic motion.

A

True

B

False

Consider the following statement for a ball falling in a viscous fluid: a) The viscous force is directly proportional to the radius of the ball b) The viscous force is directly proportional to the velocity of the ball c) The viscous force is inversely proportional to the radius of the ball d) The viscous force is inversely proportional to the velocity of the ball Which of the above statements are correct?

A

Both a and b are correct

B

Both a and d are correct

C

Both b and c are correct

D

Both c and d are correct

A particle in uniform circular motion is projected on its diameter. The motion of projection will be simple harmonic. Select the correct option regarding speed and acceleration of the particle in circular motion.

A

Speed is constant, acceleration is zero

B

Speed is constant, acceleration is non-zero

C

Speed changes, acceleration is non-zero

D

Speed changes, acceleration is zero

A particle in simple harmonic motion is described by the displacement function x(t)=Acos⁡(ωt+θ). If the initial (t=0) position of the particle is 1cm and its initial velocity isπcm/s, what is its amplitude? The angular frequency is the particle is πrad/s.

A

1 cm

B

√2 cm

C

2 cm

D

2.5 cm

The acceleration of the particle moving with simple harmonic motion is inversely proportional to the displacement of the particle from the mean position.

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