At the instantaneous center, the velocity of the moving lamina at any instant is

The moment of inertia of a circular lamina of diameter ‘d’, about an axis perpendicular to the plane of the lamina and passing through its centre, is

A

$$\frac{{\pi {{\text{d}}^4}}}{{12}}$$

B

$$\frac{{\pi {{\text{d}}^4}}}{{16}}$$

C

$$\frac{{\pi {{\text{d}}^4}}}{{24}}$$

D

$$\frac{{\pi {{\text{d}}^4}}}{{32}}$$

E

$$\frac{{\pi {{\text{d}}^4}}}{{36}}$$

A body of mass ‘m’ moving with a constant velocity ‘v’ strikes another body of same mass moving with same velocity but in opposite direction. The common velocity of both the bodies after collision is

A

v

B

2v

C

4v

D

8v

If two currents are in the same direction at any instant of time in a given branch of a circuit, the net current at that instant

A

Is zero

B

Is the sum of the two currents

C

Is the difference between the two currents

D

Cannot be determined

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

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

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

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

The center of gravity of a uniform lamina lies at

A

The center of heavy portion

B

The bottom surface

C

The mid point of its axis

D

All of the above

Instantaneous center is at infinity when the angular velocity is

A

Constant

B

Zero

C

Maximum

D

Minimum

The flow in which the particles of a fluid attain such velocities that varies from point to point in magnitude and direction as well as from instant to instant, is known as

A

One dimensional flow

B

Uniform flow

C

Steady flow

D

Turbulent flow

একটি ট্রেনের স্থির অবস্থায় দৈর্ঘ্য হলো 100 m। এটি অতি উচ্চ বেগে 80m দৈর্ঘ্যের একটি সুড়ঙ্গের মধ্য দিয়ে যায়। সুড়ঙ্গের দুই প্রান্তে অবস্থিত পর্যবেক্ষকরা লক্ষ করেন যে, একটি মুহূর্তে ট্রেনটির দৈর্ঘ্য ঠিক সুড়ঙ্গের দৈর্ঘ্যের সমান হয়। c এর এককে ট্রেন এর বেগ কত? (A train has a rest length of 100 m. Traveling at a very high velocity, it goes through a tunnel of length 80 m. Observers located at both ends of the tunnel note that at one instant the train appears to exactly fit within the tunnel. What is the velocity of the train expressed in units of c?)

A

0.866 c

B

0.333 c

C

0.5 c

D

0.6 c

The acceleration of a particle moving with simple harmonic motion, at any instant is given by

A

$$\omega {\text{y}}$$

B

$${\omega ^2}{\text{y}}$$

C

$$\frac{{{\omega ^2}}}{{\text{y}}}$$

D

$${\omega ^3}{\text{y}}$$

At the instantaneous center, the velocity of the moving lamina at any instant is

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