Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Gravitation question

2023 · 8 Apr · Shift 2 · Q48
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Gravitation
  5. /2023 · 8 Apr · Shift 2 · Q48

Gravitation question

2023 · 8 Apr · Shift 2 · Q48

JEE MainPhysicsGravitationMCQ+4 / −1
The acceleration due to gravity at height hhh above the earth if h<<Rh \lt \lt \mathrm{R}h<<R (Radius of earth) is given by
  1. A
    g′=g(1−2hR)g^{\prime}=g\left(1-\frac{2 h}{R}\right)g′=g(1−R2h​)
  2. B
    g′=g(1−2h2R2)g^{\prime}=g\left(1-\frac{2 h^{2}}{R^{2}}\right)g′=g(1−R22h2​)
  3. C
    g′=g(1−h22R2)g^{\prime}=g\left(1-\frac{h^{2}}{2 R^{2}}\right)g′=g(1−2R2h2​)
  4. D
    g′=g(1−h2R)g^{\prime}=g\left(1-\frac{h}{2 R}\right)g′=g(1−2Rh​)
View written solutionFree

Correct answer: A

  1. Acceleration due to gravity at height hhh

    At a distance R+hR+hR+h from the center of the Earth, g′=GM(R+h)2g' = \frac{GM}{(R+h)^2}g′=(R+h)2GM​

    On the surface of the Earth, g=GMR2g = \frac{GM}{R^2}g=R2GM​

  2. Relate g′g'g′ and ggg

    Dividing the two expressions, g′g=R2(R+h)2=(RR+h)2\frac{g'}{g} = \frac{R^2}{(R+h)^2} = \left(\frac{R}{R+h}\right)^2gg′​=(R+h)2R2​=(R+hR​)2

    So, g′=g(RR+h)2g' = g\left(\frac{R}{R+h}\right)^2g′=g(R+hR​)2

  3. Use the approximation h≪Rh \ll Rh≪R

    Write g′=g(11+hR)2g' = g\left(\frac{1}{1+\frac{h}{R}}\right)^2g′=g(1+Rh​1​)2

    Using the binomial approximation, (1+x)−2≈1−2xfor x≪1\left(1+x\right)^{-2} \approx 1-2x \quad \text{for } x \ll 1(1+x)−2≈1−2xfor x≪1

    Here, x=hRx = \frac{h}{R}x=Rh​, so g′≈g(1−2hR)g' \approx g\left(1-2\frac{h}{R}\right)g′≈g(1−2Rh​)

  4. Match with the options

    This is exactly: g′=g(1−2hR)g' = g\left(1-\frac{2h}{R}\right)g′=g(1−R2h​)

    Therefore, the correct option is A.

PreviousNext

More from Gravitation

  • The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new…2023 · MCQ
  • Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is2023 · MCQ
  • Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=2R​ from the surface of earth, if its weight on the surface of earth is 200 N, will be: (Given R = radius of earth)2023 · MCQ
  • If the earth suddenly shrinks to 641​ th of its original volume with its mass remaining the same, the period of rotation of earth becomes x24​ h. The value of x is ​.2023 · Numerical
  • The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given g=π2 m/s2,R= radius of earth)2023 · MCQ
  • Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at…2023 · MCQ
  • The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are ρ and ρ/3 respectively. The ratio of acceleration due to gravity at their surfaces (gA​:gB​) will be:2023 · MCQ
  • A space ship of mass 2×104 kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10 m/s2…2023 · MCQ