A particle inside a hollow sphere of radius r, having coefficient of friction µ can rest up to height of

The radius of a friction circle for a shaft rotating inside a bearing is (where r = Radius of shaft and $$\tan \varphi $$ = Coefficient of friction between the shaft and bearing)

A

$${\text{r}}\sin \varphi $$

B

$${\text{r}}\cos \varphi $$

C

$${\text{r}}\tan \varphi $$

D

$$\frac{{\text{r}}}{2}\cos \varphi $$

A hollow sphere and a solid sphere of the same material and equal radii are heated to the same temperature. In this case,

A

The cooling rate will be the same for the two spheres and hence the two spheres will have equal temperatures at any instant

B

Both the spheres will emit equal amount of radiation per unit time in the beginning

C

Both will absorb equal amount of radiation from the surrounding in the beginning

D

Both B & C

For a shoe brake, the equivalent coefficient of friction is equal to (where $$\mu $$ = Actual coefficient of friction and $$\theta $$ = Semi-block angle)

A

$$\frac{{2\mu \sin \theta }}{{\theta + \sin \theta }}$$

B

$$\frac{{\mu \sin \theta }}{{2\theta + \sin 2\theta }}$$

C

$$\frac{{4\mu \sin \theta }}{{\theta + \sin \theta }}$$

D

$$\frac{{4\mu \sin \theta }}{{2\theta + \sin 2\theta }}$$

Sphericity is the ratio of the surface area of a spherical particle having the same volume as the particle to the surface area of the particle. Which of the following has the maximum value of sphericity?

A

Sphere

B

Cube

C

Cylinder (L/D = 1)

D

Raschig rings

A friction circle is a circle drawn when a journal rotates in a bearing. Its radius depends upon the coefficient of friction and the

A

Magnitude of the forces on journal

B

Angular velocity of journal

C

Clearance between journal and bearing

D

Radius of journal

The surface area of hollow cylinder with radius 'r and height 'h' is measured by-

A

2πr-h

B

2πr+h

C

πrh

D

2πrh

The C.G. of a thin hollow cone of height ‘h’, above its base lies on the axis, at a height of

A

$$\frac{{\text{h}}}{3}$$

B

$$\frac{{\text{h}}}{4}$$

C

$$\frac{{2{\text{h}}}}{3}$$

D

$$\frac{{3{\text{h}}}}{4}$$

একটি কণা t = 0 সময়ে স্থির অবস্থা থেকে যাত্রা শুরু করে। কণাটির ওপর প্রযুক্ত লব্ধি বল, সময় t এর সমানুপাতিক। কণাটির গতিশক্তি নিচের কোনটির সমানুপাতিক হবে? (A particle starts from rest at t = 0. The net force acting on the particle is proportional to time t. Its kinetic energy is proportional to which one of the following?)

A

t2

B

t3

C

t

D

t4

One end of an elastic string of natural length / and modulus X is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance x, held at rest and then released. The motion is

A

a simple harmonic motion

B

a rectilinear motion with constant speed

C

a damped oscillatory motion

D

none of the above

Equivalent diameter of a particle is the diameter of the sphere having the same

A

Ratio of surface to volume as the actual volume

B

Ratio of volume to surface as the particle

C

Volume as the particle

D

None of these

A particle inside a hollow sphere of radius r, having coefficient of friction µ can rest up to height of

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