Gravitation
Multiple Choice Questions
1. Two objects of different masses falling freely near the surface of moon would
(a) have same velocities at any instant
(b) have different accelerations
(c) experience forces of same magnitude
(d) undergo a change in their inertia
Answer Answer is (a) have same velocities at any instant Explanation: Acceleration of an object depends on acceleration due to gravity irrespective of its mass. Hence object under free fall have the same velocities.Show Answer
(a) is same on equator and poles
(b) is least on poles
(c) is least on equator
(d) increases from pole to equator
Answer Answer is (c) is least on equator Explanation: The value of acceleration due to gravity is least on equator because distance between surface of the earth and its centre is more on equator than in poles.Show Answer
(a) $F / 4$
(b) $F / 2$
(c) $F$
(d) $2 F$
Answer Answer is (a) F/4Show Answer
(b) will move along a straight line towards the centre of the circular path
(c) will move along a straight line tangential to the circular path
(d) will move along a straight line perpendicular to the circular path away from the boy
Answer Answer is (c) will move along a straight line tangential to the circular path Explanation: At any instance of time object in circular motion tend to be in rectilinear motion. Object keeps on moving due to centripetal force and it moves along a straight line tangential to the circular path when strings breaks.Show Answer
(a) $d 1>d 2>d 3$
(b) $d 1>d 2<d 3$
(c) $ d 1< d 2 >d 3 $
(d) $ d1 < d2 < d3 $
Answer Answer is (d) $d 1<d 2<d 3$Show Answer
(a) depends on the value of $g$ at the place of observation
(b) is used only when the earth is one of the two masses
(c) is greatest at the surface of the earth
(d) is universal constant of nature
Answer Answer is (d) is universal constant of nature Explanation: $G$ is called as Newton’s constant. It is the force of gravity on a body. Value of G is $6.66 \times 10^{-11} Nm^{2} kg^{-2}$Show Answer
(a) the earth and a point mass only
(b) the earth and Sun only
(c) any two bodies having some mass
(d) two charged bodies only
Answer Answer is (c) any two bodies having some massShow Answer
(a) depends on mass of earth only
(b) depends on radius of earth only
(c) depends on both mass and radius of earth
(d) is independent of mass and radius of the earth
Answer Answer is (d) is independent of mass and radius of the earth Explanation: $G$ is an universal constant hence it is independent of mass and radius of the earth.Show Answer
(a) 14 times
(b) 4 times
(c) 12 times
(d) unchanged
Answer Answer is (b) 4 times Explanation: $F=Gx \dfrac{m 1 x m 2}{r 2}$ $F=Gx \dfrac{2 m 1 x 2 m 2}{r 2}$ $F=4 xGx \dfrac{{ }^{m 1 x m 2}}{r 2}$Show Answer
(a) gravity
(b) wind
(c) clouds
(d) earth’s magnetic field
Answer Answer is (a) gravityShow Answer
(a) gravitational potential
(b) acceleration due to gravity
(c) gravitational field
(d) universal gravitational constant
Answer Answer is (d) universal gravitational constant Explanation: $F=Gx \dfrac{m 1 x m 2}{r 2}$ Here point masses are separated by unit distance Hence $m 1, m 2$ and $r=1$ Hence $F=G$ which is a universal constant hence answer is universal gravitational constantShow Answer
(a) zero
(b) infinite
(c) $\mathbf{R}$ times the weight at the surface of the earth
(d) 1/R2 times the weight at surface of the earth
Answer Answer is (a) zero Explanation: At the centre of the earth acceleration due to gravity is zero. Since weight is the product of mass and gravity. Weight of object at the centre of the earth will be zero.Show Answer
(a) $2 N$
(b) $8 N$
(c) $10 N$
(d) $12 N$
Answer Answer is (a) $2 N$ Explanation: Object of weight displace $d$ by liquid = weight in air- weight in liquid $=10 N-8 N$ $=2 N$Show Answer
(a) maximum when length and breadth form the base
(b) maximum when breadth and width form the base
(c) maximum when width and length form the base
(d) the same in all the above three cases
Answer Answer is (b) maximum when breadth and width form the base Explanation: Surface area and pressure are inversely proportional. Pressure will be maximum when surface area is minimum hence the answer is maximum when breadth and width form the base.Show Answer
(a) $F 1$ is very much greater than $F 2$
(b) F2 is very much greater than $F 1$
(c) F1 is only a little greater than F2
(d) F1 and F2 are equal
Show Answer
Answer
Answer is (d) F1 and F2 are equal
Explanation:
Netwon’s third law of motion states that for every action there is equal and opposite reaction. Hence F1 and F2 are equal.
Short Answer Questions
16. What is the source of centripetal force that a planet requires to revolve around the Sun? On what factors does that force depend?
Answer Gravitational force is the source of centripetal force required to revolve around the sun. This force depends on distance between the planet and sun along with their masses.Show Answer
Answer Both the stones reach the ground simultaneously as they are dropped from same height and their intial velocity will be same .Show Answer
Answer If there is no gravitational pull from the earth moon start to move in a straight line tangent to its circular path.Show Answer
Answer Value of $g$ is greater than value of $g$ in poles. Since packets are thrown from same height packet thrown froom poles reaches the earth first.Show Answer
Answer Weight of person is $=1 / 6^{\text{th }}$ of weight on earth This proves acceleration due to gravity on moon is $1 / 6^{\text{th }}$ of acceleration due to gravity on earth. Hence the person can lift a mass 6 times heavier on moon than on earth.Show Answer
Answer $g=\dfrac{G M}{R^{2}}$ $\dfrac{M=gR^{2}}{G}$ Density of earth $D=\dfrac{\text{ Mass }}{\text{ Volume }}$ $
=\dfrac{Gr^{2}}{GxVe}
$ $
\begin{aligned}
& =\dfrac{gR^{2}}{G_3^{4} \pi R^{3}} \\
& =\dfrac{3 g}{4 \mu GR}
\end{aligned}
$Show Answer
Show Answer
Answer
Sun provides enough centripetal force to keep earth in its orbit and the earth provides centrifugal force due to its motion. These two force balance each other which prevents earth from falling into sun.
Long Answer Questions
23. How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?
Answer Let $R$ and $M$ be the radius and mass of the earth Then Weight of the object $=\dfrac{M}{R^{2}}$ Original weight $W_0=mg=mg \dfrac{M}{R^{2}}$ Hypothetically $4 m$ and $R$ becomes $\underline{R}$ Then, weight $=m G \underline{4 M}$ $
\begin{aligned}
& (\dfrac{R}{2})^{2} \\
= & (16 mg) \dfrac{M}{R^{2}} \\
= & 10 xW_0
\end{aligned}
$ Weight will be 16 times.Show Answer
Answer Force of attraction between two masses separated by distance $r$ is given by Newton law of gravitation where $F=\dfrac{G m 1 m 2}{R^{2}}$ Where $G$ is gravitational force and it is an universal constant. Gravitational force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between them. Bodies thrown from same height fall with same speed irrespective of their mass. This is due to acceleration due to gravity. $g=\dfrac{GM}{R^{2}}$ Where $M$ is mass $R$ is radius of the earth This equation shows that acceleration due to gravity depends on mass of the earth and radius of the earth. Henec tow brick tied will not fall faster than single one.Show Answer
Answer $h 1=\dfrac{1}{2} gt^{2} 1$ $h 2=\dfrac{1}{2} gt^{2} 2$ as $x=o$ $\dfrac{t 1}{t 2}=\sqrt{\dfrac{h 1}{h 2}}$ As the acceleration remain same ratio between two objects remain same. In this case acceleration does not depend upon mass and size.Show Answer
(b) A ball weighing $4 kg$ of density $4000 kg m-3$ is completely immersed in water of density $103 kg m-3$ Find the force of buoyancy on it. (Given $g=10 m s-2$.)
Show Answer
Answer
i) Buoyant force, $F=Vpg$
$p=$ Density of water, $V=$ Volume of water displaced by the body
Volume and density of an object decides its Buoyancy. Cube will experience a greater byoyancy in saturated solution. If cube is reduces to $4 cm$ on each side, volume of cube becomes less as the buoyancy will be reduced as buoyant force is directly proportional to volume.
(ii) The magnitude of the buoyant force given by $F=Vpg$
where $V=$ Volume of body immersed in water or volume of water displaced, $p=$ Density of liquid.
$[\therefore.$ Given, mass of a ball $=4 kg$, density $.=4000 kgm^{-3}]$.
Hence Volume of solid $=\dfrac{\text{ Mass }}{\text{ Density }}$
$ \begin{aligned} & =\dfrac{4}{4000} \\ & =\dfrac{1}{1000} \\ & \text{ Buoyancy F= Vpg } \\ & =\dfrac{1}{1000} \times 1000 \times 10 \\ & =10 N \end{aligned} $
