GREEN PARK COACHING CENTRE, NAMAKKAL

CRASH COURSE - PHYSICS WORKSHEET

Choose the correct answer :

1 th 3 GM 2 3 GM 2
1. If the earth were suddenly contract to of 3) 4)
n 4 R2 R2
its present size without any change in its mass, 6. Three solid spheres each of mass ‘m’ and
the duration of the new day is nearly radius R are released from the position shown
1) (24 / n) hr 2) (24n) hr in figure. The speed of any one sphere at the
2
3) (24 /n ) hr 4) (24 n2) hr time of collision would be
2. Figure shows the elliptical path of a planet
about the sun. The two shaded parts have
equal area. If t1 and t2 be the time taken by the
planet to go from a to b and from c to d
respectively, then
1 3  3 1 
1) Gm    2) Gm   
d R d R
 2 1  1 2
3) Gm    4) Gm   
1) t1 < t2 2) t1 = t2 R d R d
3) t1 > t2 4) insufficient data 7. The force between two identical particles
3. Time period of revolution of a nearest satellite separated by distance d is F. Four such
around a planet of radius R is T. Period of identical particles are placed at the corners of
revolution around another planet, whose a square of side d. The magnitude of net force
radius is 4R but having same density is on any particle will be
1) T 2) 4T 1) zero 
2) 1  2 2 F
3) 16T 4) 3 3T
4. Satellites A and B are orbiting around the 
3) 1  2 2  F2 4) 1  2  F
earth in orbits of radius R and 9R respectively.
The ratio of their areal velocities is 8. Two metal spheres each of radius ‘r’ are kept
in contact with each other. If ‘d’ is the density
1) 1 : 1 2) 1 : 3
of the sphere material, the gravitational force
3) 1 : 9 4) 1 : 2 between those spheres is proportional to
5. Three uniform spheres of mass M and radius 1) d2r6 2) d2r4
R each are kept in such a way that each 3) d2/r4 4) r4/d2
touches the other two. The magnitude of the 9. Suppose a vertical tunnel is dug along the
gravitational force on any of the spheres due diameter of the earth assumed to be a sphere
to the other two is of uniform mass having density . If a body of
3 GM 2 3 GM 2 mass m is thrown in this tunnel, its
1) 2) acceleration at a distance y from the centre is
2 R2 2 R2
given by
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1) 2)

4 3
1) g y 2)  G y
3 4
4 4
3) y 4) G y 3) 4)
3 3
10. A man weighs 80 kg on the surface of earth of
radius R. At what height above the surface of 14. An infinite number of masses, each of 1 kg,
earth his weight will be 40 kg? are placed on the positive x-axis at 1m, 2m,
R 4m, 8m,…… from the origin. The value of the
1) 2) 2 R gravitational field at the origin due to this
2
distribution is
3) ( 2  1)R 4) ( 2  1)R 4G
11. If earth is supposed to be a sphere of radius R, 1) 2G 2)
3
if g30 is value of acceleration due to gravity at 3G
3) 4) 
latitude of 30o and g at the equator, the value 4
of g – g30o is 15. A solid sphere of mass M and radius ‘a’ is
surrounded by a uniform concentric spherical
R
2
3 R
2
1) 2) shell of radius 2a and mass 2M. The
4 4 gravitational field distance 3a from the centre
2 R will be
3) 2R 4)
2 2GM GM
1) 2
2)
12. The ratio between the values of acceleration 9a 3a 2
GM 2GM
due to gravity at a height 1 km above and at 3) 2
4)
depth 1 km below the earth’s surface is 9a 3a 2
16. A body starts from rest from a point at a
(R = radius of earth)
distance r0 from the centre of the earth. It
R2 R reaches the surface of the earth whose radius
1) 2)
R R 1 is R. The velocity acquired by the body is
R2 2R
3) 4) 1 1 1 1
R 1 R 1 1) 2GM  2) 2GM   
R r0  R r0 
13. A spherically symmetric gravitational system
of particles has a mass density 1 1 1 1 
3) GM  4) GM   
  0 for r  R
0 for r  R where 0 is a constant. A test R r0  R R0 
mass can undergo circular motion under the 17. The change in the gravitational potential
energy when a body mass ‘m’ is raised to a
influence of the gravitational field of particles.
height nR above the surface of the earth is
Its speed ‘v’ as a function of distance r (0 < r <
(here R is the radius of the earth)
) from centre of the system is represented by
 n   n 
1)   mgR 2)   mgR
 n 1   n 1 
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mgR 22. The magnitude of the potential energy per unit
3) nmgR 4)
n mass of the object at the surface of earth is E.
18. Two bodies of masses m1 and m2 are initially Then the escape velocity of the object is
at rest placed infinite distance apart. They are 1) 2E 2) 2 E
then allowed to move towards each other
E
under mutual gravitational attraction. Their 3) E 4)
2
relative velocity when they are ‘r’ distance
23. A geo-stationary satellite is orbiting the earth
apart is
at a distance of 7R from the centre of earth, R
2G(m1  m 2 ) 2Gm1m 2 being the radius of earth. The time period of
1) 2)
r (m1  m 2 )r another satellite at a height of 2.5 R from the
G(m1  m 2 ) Gm1m 2 surface of earth is
3) 4)
r (m1  m 2 )r 1) 6 2 hr 2)
6
hr
19. A projectile is projected with velocity ave in 2
vertically upward direction from the ground 3) 6 hr 4) 10 hr
into the space (ve is escape velocity and a < 1) 24. If mean radius of earth is R, its angular
If air resistance is considered to be negligible
velocity is  and the acceleration due to
then the maximum height from the centre of
earth to which it can go, will be H (R is radius gravity at the surface of the earth is ‘g’, then
of the earth) then the value of ‘a’ is the cube of the radius of the orbit of
HR H geostationary satellite will be
1) 2)
H R H R 2g R 2g
1) 2)
H HR 2 
3) 4)
HR H R 22 Rg
20. The gravitational field in a region is given by 3) 4)
g 2
E  3iˆ  4ˆj N/kg. Find gravitational potential
25. A satellite of mass ‘m’ is circulating around
at a point (2, 0). If the potential at the origin is
taken as zero. the earth with constant angular velocity. If
radius of the orbit is r and mass of the earth is
Nm Nm
1) 5 2) 6 M, the ratio of kinetic energy and angular
kg kg
momentum of the satellite about the centre of
Nm
3) 0 4) 7 earth will be
kg
m GM 1 GM
21. Four equal masses each of mass M are placed 1) 2)
2 r 2 r3
at the corners of a square of side ‘a’. The
escape velocity of a body from the centre ‘O’ M Gm GM
3) 4)
of the square is 2 r2 r3

2GM 8 2GM
1) 4 2)
a a

4 GM 4 2 GM
3) 4)
a a
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ANSWER KEY
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

3 2 1 2 3 4 3 2 4 3 2 3 3 2 2

16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

2 1 1 4 2 2 1 1 1 2