Gravitational Field Due to a Shell

Q. for what value of x gravitational field is maximum on the axis of ring ? 1) R/\sqrt3 2) R/\sqrt2 3) R 4) at cente

Q.

What is the intensity of gravitational field of the centre of a spherical shell

1. 

2. Zero

3. None of these

4. g

Q. In the following two exercises, choose the correct answer from among the given ones: The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a, (ii) b, (iii) c, (iv) 0.

Q. 43.A cylinder of weight w is resting on a fixed V-groove as shown in figure.Calculate normal reactions between the cylinder and two inclined walls. Options- (A) w, w (B) w/2, w/2 (C) w, w/2 (D) w/2, w

Q. If a tunnel is cut at any orientation through earth, then find the time taken by a ball released from one end to reach the other end. (neglect earth rotation and take radius of earth as $R=64\times {10}^5\text{m}$ and $g=10{\text{m/sec}}^2$)

1. 
   depend on orientation
2. 
   $41.9\text{minutes}$
3. 
   $8\text{minutes}$
4. 
   $84.6\text{minutes}$

Q. 74.2 identical cylindrical vessels with their bases at same level contains a liquid of density "p". The height of the liquid in one vessel is h1 and that in the other vessel is h2. The area of either base is A. The work done by gravity in equalizing the levels when the 2 vessels are connected is____.

Q. Choose the correct alternative :
(a) Acceleration due to gravity increases/decreases with increasing altitude.
(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula $-GMm(1/r_2-1/r_1)$ is more/less accurate than the formula $mg(r_2-r_1)$ for the difference of potential energy between two points $r_2$ and $r_1$ distance away from the center of the earth.

Q. 138.Find the work done by external agent to fill the mass m in a spherical volume of radius R.

Q. Intensity of gravitational field inside hollow uniform spherical shell

1. is zero at center but nonzero at other points.
2. is nonzero at all points.
3. is zero at all points because variables regims of shell attracts point mass in various directions, these forces cancel each other completely.
4. is non uniform & varies linearly.

Q. An earth satellite $S$ has an orbit radius which is $4$ times that of a communication satellite $C$. The period of revolution of $S$ is

1. 4 days
2. 8 days
3. 16 days
4. 32 days

Q.

What is the intensity of gravitational field of the centre of a uniform spherical shell

1. $\frac{Gm}{r^2}$

2. g

3. Zero

4. None of these

Q. Let V and E be the gravitational potential and gravitational field at a distance r from the centre of a uniform spherical shell. Consider the following two statements:
(A) The plot of V against r is discontinuous.
(B) The plot of E against r is discontinuous.
(a) Both A and B are correct.
(b) A is correct but B is wrong.
(c) B is correct but A is wrong.
(d) Both A and B are wrong.

Q. 3) Dependence of intensity of gravitational field (E) ofearth with distance (r) from centre of earth isAIPMT-2014\rbrack correctly respresented by