TOPIC

GRAVITATION
17
SECTION -|: STRAIGHT OBJECTIVE TYPE
m at
17.1
the diameter of the earth (Radius R& mass M), There is a particle of mass
W
the centre thealong
e 3 ofdug tunnel. The minimum velocity aiven to the particle so that it just reaches to the surtace
of the earth is

GM GM |2GM
(A) R (B) 2R (C) R
(D) it wil reach with the help of negligible velocity.
17.2 A cavity of radius RI2 is made inside a solid sphere of radius R. The centre of the cavity is located ial a
distance RI2 from the centre of the sphere. The gravitational force on a particle of mass m aa
distance R/2 from the centre of the sphere on the line joining both the centres of sphere and cavity is
(opposite to the centre of cavity).
[Here g =GM/R, where Mis the mass of the sphere without cavity ]
(A
mg 3 mg mg (D) none of these
(B) 8 (G) 16
17.3 Asatellite is launched in the equatorial plane in such a way that it can transmit signals upto 60
latitude on the earth. The angular velocity of the satellite is
GM GM GM 3V3GM
(A) BR (C) 4R (D)
(B)2R 8R

17.4 Asatelite is seen after each 8 hours over equator at a place on the earth when its sense of rotation is
opposite to the earth. The time interval after which it can be seen at the same place when the sense of
rotation of earth & satellite is same will be :
(A) 8 hours (B) 12 hours (C) 24 hours (D) 6 hours

17.5 Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction
because of their mutual gravitational attractive force. Velocity of a particle is given by

(A) Gm (B) Gm 1 Gm1+ N2

4 (C) (D)
2r 2

17.6 The gravitational potential of two homogeneous spherical shells Aand B of same surface density at their
respective centres are in the ratio 3:4. if the two shells coalesce into single one such that surface densly
remains same, then the ratio of potential at an internal point of the new shell to shell A is equal to
(A) 3:2 (B) 4:3 (C) 5:3 (D) 5:6
 17.7 Apoint P lies on the axis of a fixed ring of mass Mand radius R, at a distance 2R from its centre O. A
small particle starts from P and reaches O under gravitational attraction only. Its speed at O will be
2GM 1
(A) zero (B) R (C) 2GM5-1)
R (D)
|2(1-E
17.8 Gravitationai field at the centre of a semicircle formed by a thin wire AB of mass mand length t is :

Gm Gm
(A)2 along +x axis (B),2 along +y axis

2n Gm 2n Gm
(C)2 along +x axis ( 2 along +y axis

17.9 The percentage change in the acceleration of the earth towards the sun from a total ecipse of the sun
to the point where the moon is on a side of earth directly opposite to the sun is
M, 2100 Mm x100
(A) (B) M,(2100
M M100
17.10 Aparticle of mass Mis at a distance 'a' from surface of athin same spherical shell of uniform equal mass and
having radius a.
M

(A) Gravitational field &potential both are zero at centre of the shell
(B) Gravitational field is zero not only inside the shell but at a point outside the shell also
(C) Inside the shell, gravitational field alone is zero
(D) Neither gravitational field nor yravilational potential is zero inside the shell.
Asmall area is removed from a uniform spherical shell of mass Mand radius R. Then the gravitational
17.11
field intensity near the hollow portion is
GM GM 3GM
(D) Zero
(A) R? (B) 2R (©) 9p2
17.13 Two particles of combined mass M, placed in space with certain separation, are released. Interaction between
of one particle
the particles is only of gravitational nature and there is no external force present. Acceleration
a mnagnitude:
with respect to the other when separation between them is R, has
GM GM
(A)
2R? (B) R
2GM (D) not possible to calculate due to lack of information
C)

from earth's
17.14 Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity
Surface is :
(A) RI2 (B) 16R/9 (C) RI3 (D) R/B
SECTION - VI: INTEGER TYPE
on an
17.23 Ravi can throwa ball at a speed on earth which can cross a river of width 10 m. Ravi reaches
of planet so
imaginary planet whose mean density is twice of the earth. if maximum possible radius
x is. (Given radius
that if Ravi throws the ball at same speed it may escape from planet.is x km. then
of earth = 6.4 x 10 m.)
(in joule) in displacing
17.24 The gravitational field in a region is given byE= (3i - 4j) N/kg. Find out the work done
+ 9.
a particle by 1 m along the line 4y = 3x
4R from the centre of the earth, with speed V,
17.25 Aparticle is projected from point A, that is at a distance and point A, as shown in the fiqure.
in a direction making 30° with the line joining the centre of the earth Consider gravitational interaction
Findthe speed V, if particle passes grazing the surface of the earth.
GM =6.4 x 10' m/s?)
only between these two. (use R

Express your answer in the form of km/sec and fill value of X.