CBSE Questions for Class 11 Engineering Physics Gravitation Quiz 9 - MCQExams.com

Which of the following statements are true about acceleration due to gravity?
  • g decreases in moving away from the centre if r $$>$$ R
  • g decreases in moving away from the centre if r $$<$$ R
  • g is zero at the centre of earth
  • g decreases if earth stops rotating on its axis
A projectile is fired vertically upwards from the surface of the earth with a velocity $$kv_e$$ where $$v_e$$ is the escape velocity and $$k < 1$$. If R is the radius of the earth, the maximum height to which it will rise measured from the centre of earth will be (neglect air resistance).
  • $$\dfrac{1-k^2}{R}$$
  • $$\dfrac{R}{1-k^2}$$
  • $$R(1-k^2)$$
  • $$\dfrac{R}{1+k^2}$$
A man weighs $$80$$kg on the surface of earth of radius R. At what height above the surface of earth his weight will be $$40$$kg?
  • $$2637.6km$$
  • $$3.675km$$
  • $$8765km$$
  • $$(\sqrt{2}+1)R$$
Which of the following laws are conserved, if the areal acceleration is zero
  • Law of conservation of angular velocity
  • Law of conservation of angular momentum
  • Law of conservation of angular acceleration
  • Law of conservation of angular displacement
The value of universal gravitational constant on earth for a particle of mass 5 kg is 
  • $$6.67 \times 10^{-11}$$
  • $$6.67 \times 10^{-7}$$
  • $$5 \times 6.67 \times 10^{-11}$$
  • $$6.67 \times 10^{-23}$$
Two identical particles of mass $$m$$ are placed at a distance $$r$$ from each other. If their separation is doubled, then the effect on gravitational constant will be 
  • Gravitational constant remains same
  • Gravitational constant becomes quadrupled
  • Gravitational constant becomes 1/4th of the actual one
  • Gravitational constant becomes doubled
The areal velocity of an object of mass m=2 kg revolving around another object is given by $$2m^2/s$$, what is the angular momentum of the particle
  • $$6 kg-m^2/s$$
  • $$8 kg-m^2/s$$
  • $$4 kg-m^2/s$$
  • $$2 kg-m^2/s$$
If the gravitational constant is expressed in terms of $$dynes\ m^{-2} kg^{2}$$, how will the value of G change:
  • $$6.67 \times 10^{-11} dynes \ kg^2 m^{-2}$$
  • $$6.67 \times 10^{-8} dynes \ kg^2 m^{-2}$$
  • $$6.67 \times 10^{-6} dynes \ kg^2 m^{-2}$$
  • $$6.67 \times 10^{-3} dynes \ kg^2 m^{-2}$$
A particle of mass M is placed at origin and a small mass m is placed at A, at a distance of r from M. A force F is applied to m to make it move from A to a nearby point B. When the force becomes zero, it is observed that the mass m moves from B back to A. This is due to the reason
  • Potential of B is larger than potential of A
  • Objects starts moving in gravitational field until constant potential difference exist
  • The line B to A is equipotential surface
  • The mass moves from B to A, since A is nearer to origin
Linear momentum of the planet is
988178_7e421964f4f744d0af68d9d081fbcab7.png
  • Different for different points of the orbit
  • Conserved
  • Not conserved
  • None of these
The weight (W) of an object at a depth of R/4 from the surface of the earth will be (R is the radius of the earth)
  • Zero
  • W/4
  • W/2
  • W
A spring balance is graduated on sea level. If a body of mass 5 kg is weighed with this balance and the balance is taken to a height of 360kms and the object is weighed again, then the weight of the object
  • Will be more than 5 kg
  • Will be less than 5 kg
  • Will remain same
  • Will first increase and then decrease
At what height over the earths pole, the free fall acceleration decreases by one percent (assume the radius of earth to be 6400 km)            
  • 32 km
  • 80 km
  • 1.293 km
  • 64 km
The gravitational potential energy is the
  • work done in bringing an object from infinity to radius r
  • work done in moving an object around the earth
  • work done by an object in attaining an object's acceleration equal to $$9.8 m/s^2$$
  • work done in moving an object between two points horizontally
 The variation of acceleration due to gravity $$g$$ with distance $$d$$ from centre of the earth is best represented by ($$R=$$Earths radius):
 The height at which the acceleration due to gravity becomes $$g/9$$ (where $$g=the$$ acceleration due to gravity on the surface of the earth) in terms of $$R$$, the radius of the earth, is
  • $$R/2$$
  • $$\sqrt { 2 } R$$
  • $$2R$$
  • $$\dfrac { R }{ \sqrt { 2 } }$$
The fractional change in the value of free-fall acceleration $$'g'$$ for a particle when it is lifted from the surface to an elevation $$h. (h < < R)$$ is
  • $$h/ R$$
  • $$-2h/ R$$
  • $$2h/ R$$
  • None of these
Gravitational potential energy is 
  • the product of force and velocity
  • the product of force and momentum
  • the product of weight and height lifted by an object
  • the product of force and displacement, if the particle is moving in a cirlce
The acceleration due to gravity at a height $$\left (\dfrac {1}{20}\right )^{th}$$ the radius of earth above earth's surface is $$9\ m/s^{2}$$. Its value at a point at an equal distance below the surface of earth is ________ $$m/s^{2}$$.
  • $$55\ m/s^{2}$$
  • $$9.5\ m/s^{2}$$
  • $$12\ m/s^{2}$$
  • $$15\ m/s^{2}$$
Escape velocity from the surface of moon is less than that from the surface of earth because the moon has no atmosphere while earth has a very dense one.
  • True
  • False
At what depth below the surface of the earth acceleration due to gravity $$'g'$$ will be half of its value at $$1600\ km$$ above the surface of the earth?
  • $$1.6\times 10^{6}m$$
  • $$2.4\times 10^{6}m$$
  • $$3.2\times 10^{6}m$$
  • $$4.8\times 10^{6}m$$
Weight of a body on earth's surface is $$W$$. At a depth half way to the centre of the earth, it will be (assuming uniform density in earth).
  • $$W$$
  • $$W/2$$
  • $$W/4$$
  • $$W/8$$
The earth, moving around the sun in a circular orbit, is acted upon by a force and hence work must be done on earth by this force.
  • True
  • False
In a double star system one of mass $$m_{1}$$ and another of mass $$m_{2}$$ with a separation $$d$$ rotate about their common centre of mass. Then rate of sweeps of area of star of mass $$m_{1}$$ to star of mass $$m_{2}$$ about their common centre of mass is
  • $$\dfrac {m_{1}}{m_{2}}$$
  • $$\dfrac {m_{2}}{m_{1}}$$
  • $$\dfrac {m_{1}^{2}}{m_{2}^{2}}$$
  • $$\dfrac {m_{2}^{2}}{m_{1}^{2}}$$
The radius of a planet is $$4$$ times the radius of the earth. The time period of revolution of the planet will be:
  • $$1\ yr$$
  • $$2\ yr$$
  • $$4\ yr$$
  • $$8\ yr$$
If a planet gets inflated, keeping its density constant, then $$g$$ will increase.
  • True
  • False
If potential at the surface of a planet is taken as zero, the potential at infinity will be $$(M$$ and $$R$$ are mass and radius of the planet).
  • Zero
  • $$\infty$$
  • $$\dfrac {GM}{R}$$
  • $$-\dfrac {GM}{R}$$
Weight of a body decreases by $$1.5$$%, when it is raised to a height $$h$$ above the surface of the earth. When the same body is taken to same depth $$h$$ in a mine, its weight will show
  • $$0.75$$% increase
  • $$3.0$$% decrease
  • $$0.75$$% decrease
  • $$1.5$$% decrease
The ratio of acceleration due to gravity at a depth $$h$$ below the surface of earth and at a height $$h$$ above the surface for $$h<< R$$
  • constants only when $$h<< R$$
  • increases linearly with $$h$$
  • increases parabolically with $$h$$
  • decreases
If R is the radius of the earth, then the ratio of acceleration due to gravity on surface of the earth to acceleration due to gravity at height nR is:
  • $$
    \left( {n + 1} \right)^{ - 1}
    $$
  • $$
    \left( {n + 1} \right)^2
    $$
  • $$
    \left( {n + 1} \right)^{ - 2}
    $$
  • $$
    \left( {n + 1} \right)^3 
    $$
The value of $$g$$ on the earths surface is $$980\ cm/{sec}^{2}$$. Its value at a height of $$64\ Km$$ from the earth's surface is
  • $$960.40\ cm/sec ^{ 2 }$$
  • $$984.90\ cm/sec ^{ 2 }$$
  • $$982.45\ cm/sec ^{ 2 }$$
  • $$977.55\ cm/sec ^{ 2 }$$
A body of mass 'm' is raised from the surface of the earth to a height 'nR' (R- radius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth)
  • $$\left( \dfrac { n }{ n+1 } \right) mgR$$
  • $$\left( \dfrac { n-1 }{ n } \right) mgR$$
  • $$\dfrac { mgR }{ n } $$
  • $$\dfrac { mgR }{ (n-1) } $$
The height of the point vertically above the earths surface at which the acceleration due to gravity becomes $$1\%$$ of its value at the surface is ($$R$$ is the radius of the earth)
  • $$9R$$
  • $$10R$$
  • $$8R$$
  • $$20R$$
At what height from the ground will be the value of $$g$$ be the same as 
that in $$10 km$$ deep mine below the surface of earth.
  • 20 km
  • 7.5 km
  • 5 km
  • 2.5 km
A particle hanging from a spring stretches it by 1 cm at earth's surface. Radius of the earth is 6400 km. At a place 800 km above the earth's surface, the same particle will stretch the spring by 
  • 0.79 cm
  • 1.2 cm
  • 4 cm
  • 17 cm
The value of acceleration due to gravity at a point P inside the earth and at another point Q outside the earth is g/2 .(g being acceleration due to gravity at the surface of the earth). Maximum possible distance in terms of radius of earth R between P and Q is:
  • $$2R$$
  • $$2R(\sqrt{2}+1)$$
  • $$\dfrac{R}{2} (2\sqrt{2}-1)$$
  • $$\dfrac{R}{2} (2\sqrt{2}+1)$$
A body weight W Newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be :
  • $$\dfrac{W}{2}$$
  • $$\dfrac{2W}{3}$$
  • $$\dfrac{4W}{9}$$
  • $$\dfrac{W}{4}$$
The height at which the value of acceleration due to gravity becomes 50% of that at the surface of the earth. (Radius of the earth = 6400 km) is (approximately) :
  • 2630
  • 2640
  • 2650
  • 2660

At what altitude (h) above the earth's surface would the acceleration due to gravity be one fourth of its value at the earths surface?

  • $$h=R$$
  • $$h=4R$$
  • $$h=2R$$
  • $$h=16R$$
A particle weights 120N on the surface of the earth. At what height above the earth's surface will its weight be 30N? Radius of the earth is 6400 km.
  • 6000
  • 6400
  • 5800
  • 7000
A particle is taken to a height $$R$$ above the surface, where $$R$$ is the radius of the earth. The acceleration due to gravity there is:
  • $$2.45\ m/s^{2}$$
  • $$4.9\ m/s^{2}$$
  • $$4.8\ m/s^{2}$$
  • $$19.6\ m/s^{2}$$
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere ?(given : Mass of oxygen $$(m) =2.76\times 10^{-26}$$ kg Boltzmann's constant $$k_B=1.38 \times 10^{-23}JK^{-1})$$ :
  • $$2.508 \times 10^4K$$
  • $$8.360 \times 10^4 K$$
  • $$5.016 \times 10^4 K$$
  • $$1.254 \times 10^4 K$$
The altitude at which the weight of a body is only $$64\%$$ of its weight on the surface of the earth is (Radius of the earth $$6,400km$$)
  • $$1600 M$$
  • $$2Km$$
  • $$160 Km$$
  • $$1600 Km$$
The height at which the weight of a body becomes $$\dfrac{1}{16^th}$$,its weight on the surface of earth (radius R), is :-
  • $$3R$$
  • $$4R$$
  • $$5R$$
  • $$15R$$
If the radius of the earth is $$6400km$$, the height above the surface of the earth ,where the value of acceleration due to gravity will be $$1\%$$ of its value from the surface of the earth is  
  • $$6400km$$
  • $$64km$$
  • $$711km$$
  • $$5760km$$
A body of mass m is taken from earth's surface to q a height equal to radius of earth . the change in potential will be 
  • $$mg$$
  • $$\dfrac{1}{2}mg R$$
  • $$2mgR$$
  • $$\dfrac{1}{4}mgR$$
At what height above the surface of earth, acceleration due to gravity is $$\Bigg \lgroup \frac{1}{8} \Bigg \rgroup^{th}$$ of its value at the surface of earth: ($$R_e$$ = Radoius of earth)
  • $$\sqrt{3}R_e$$
  • $$2R_e$$
  • $$2\sqrt{2} R_e$$
  • $$(\sqrt{3} - 1) R_e$$
Earth can be considered as uniform solid sphere of radius $$R. g_{1}$$ and $$g_{2}$$ be acceleration due to gravity at points $$R/2$$ below the surface and $$R/2$$ above the surface of earth respectively. Then $$\dfrac {g_{1}}{g_{2}}$$ equals to
  • $$\dfrac {1}{4}$$
  • $$\dfrac {1}{2}$$
  • $$\sqrt {2}$$
  • $$\dfrac {9}{8}$$
If 'R' is radius of the earth, the height above the surface of the earth where the weight of a body is $$36\%$$ less than its weight on the surface of the earth is 
  • $$\dfrac{4R}{5}$$
  • $$\dfrac{R}{5}$$
  • $$\dfrac{R}{6}$$
  • $$\dfrac{R}{4}$$
How much deep inside the earth radius should a an go ,so that his wight become on fourth of that one the earth's surface/
  • $$\dfrac{R}{4}$$
  • $$\dfrac{R}{2}$$
  • $$\dfrac{3R}{4}$$
  • $$\dfrac{2R}{3}$$
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