The most convenient co-ordinate system for specifying the relative positions of heavenly bodies on the celestial sphere, is

On the celestial sphere, what are the circles that pass through Zenith from the celestial sphere called?

A

Vertical circles

B

Latitude

C

Longitude

D

Horizon

The position of a heavenly body on the celestial sphere can be completely specified by

A

Its altitude and azimuth

B

Its declination and hour angle

C

Its declination and right ascension

D

All the above

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.
$$\iint\limits_{\text{S}} {\frac{1}{4}\left( {{\text{F}} \cdot {\text{n}}} \right){\text{dA}}}$$ where S is the sphere, x² + y² + z² = 1 and n is the outward unit normal vector to the sphere.
The value of the surface integral is

A

$$\pi $$

B

$$2\pi $$

C

$$\frac{{3\pi }}{4}$$

D

$$4\pi $$

A heavenly body revolves around a massive star in a highly elliptical orbit. Ignoring mass loss of the heavenly body when it comes too close to the star, the angular momentum over the orbit is _____________

A

Zero

B

Increasing

C

Decreasing

D

Constant

A smaller sphere has potential 50V and a larger sphere has potential 100V. How should they be placed so that if they are connected with the help of a wire, the charge will flow from the smaller sphere to the larger sphere? Both the spheres are conducting and hollow.

A

Concentrically

B

Touching each other

C

It is never possible

D

The smaller sphere should be grounded

A metal sphere of surface area 0.0225 m2 is in an evacuated enclosure whose walls are held at a very low temperature. Electric current is passed through resistors embedded in the sphere causing electrical energy to be dissipated at the rate of 75 W. If the sphere surfaces temperature is measured to be 560 K, while in steady state, calculate emissivity of the sphere surface

A

0.498

B

0.598

C

0.698

D

0.798

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is1/6ththe radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?

A

31276

B

36194

C

25182

D

33264

A sphere of radius 'R₁' is enclosed in a sphere of radius 'R₂'. The view (or shape) factor for radiative heat transfer of the outer sphere with respect to the inner sphere is

A

0

B

$$\frac{{{{\text{R}}_2}}}{{{{\text{R}}_1} + {{\text{R}}_2}}}$$

C

1

D

$${\left( {\frac{{{{\text{R}}_1}}}{{{{\text{R}}_2}}}} \right)^2}$$

During elastic impact, the relative velocity of the two bodies after impact is __________ the relative velocity of the two bodies before impact.

A

Equal to

B

Equal and opposite to

C

Less than

D

Greater than

Celestial Horizon is always the same as the Celestial Equator.

A

True

B

False

The most convenient co-ordinate system for specifying the relative positions of heavenly bodies on the celestial sphere, is

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