Gravitation — Class 11 (40 Questions)

Gravitation — Class 11 (Full 40-Question Compilation)

CBSE / ISC / WBCHSE • Conceptual, Derivations & Numericals • Chapter 7

Section A — Conceptual & Definition-Type (1–2 marks)

State Newton’s law of universal gravitation and define the gravitational constant \(G\).
Write the SI unit and dimensional formula of \(G\).
Define gravitational field and gravitational field intensity.
Distinguish between gravitational force and electrostatic force (any two differences).
What is gravitational potential energy? Why is it taken as negative?
Define gravitational potential at a point.
What is weightlessness? Explain using a freely falling elevator or an orbiting satellite.
What is a geostationary satellite? State the necessary conditions.
State Kepler’s three laws of planetary motion.
Why does gravitational potential inside a hollow spherical shell remain constant?

Derive \( g=\dfrac{GM}{R^2} \) for acceleration due to gravity at Earth’s surface.
Derive the variation of \(g\) with height \(h\): obtain \(g(h)\) in terms of \(g_0, R\) and \(h\).
Derive the variation of \(g\) with depth \(d\): obtain \(g(d)\) in terms of \(g_0, R\) and \(d\).
Derive the expression for escape velocity \(v_{\text{esc}}=\sqrt{\dfrac{2GM}{R}}\).
Show that escape velocity is independent of the mass of the escaping body.
Derive the orbital velocity of a satellite at height \(h\): \(v=\sqrt{\dfrac{GM}{R+h}}\).
Derive the total mechanical energy of a satellite in circular orbit and prove \(E=-\tfrac{1}{2}mv^2\).
Using Kepler’s third law, derive \(T^2\propto r^3\) for circular orbits.
Prove that the gravitational field inside a uniform spherical shell is zero.
Derive the gravitational potential due to a point mass: \(V=-\dfrac{GM}{r}\).

Explain again (quantitatively) why gravitational potential energy is negative.
Differentiate between gravitational field and gravitational potential (definitions + units).
Explain the phenomenon of weightlessness for an astronaut in an orbiting spacecraft.
State two limitations of Newton’s law of gravitation.
Why doesn’t an ideal circular-orbit satellite fall back to Earth?
Define the binding energy of a satellite and relate it to its orbital radius.
List the conditions required for a satellite to be geostationary and state two uses.
Distinguish between orbital velocity and escape velocity (expressions + dependence on \(R\)).
Describe how gravitational potential energy changes as a body moves from Earth’s surface to infinity.
State two important applications of artificial satellites (communication, meteorology, etc.).

Two bodies of masses \(m_1=5\,\text{kg}\) and \(m_2=10\,\text{kg}\) are separated by \(r=2\,\text{m}\). Find the gravitational force between them using \(G=6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}\).
Given \(M_E=6.0\times10^{24}\,\text{kg}\) and \(R_E=6.4\times10^6\,\text{m}\), verify that \(g=\dfrac{GM_E}{R_E^2}\approx 9.8\,\text{m\,s}^{-2}\).
Find the escape velocity from Earth’s surface using \(G=6.67\times10^{-11}\), \(M_E=6\times10^{24}\,\text{kg}\), \(R_E=6.4\times10^6\,\text{m}\).
A satellite orbits at height \(h=600\,\text{km}\). Calculate its orbital speed \(v\) and time period \(T\).
Determine the time period of a satellite at \(h=36{,}000\,\text{km}\) (geostationary orbit). Show that \(T\approx 24\) h.
At what height above Earth’s surface will \(g\) become one-fourth of its surface value? (Take \(R_E=6400\,\text{km}\).)
Find \(g'\) at a depth \(d=R/4\) below Earth’s surface using \(g'=g\!\left(1-\dfrac{d}{R}\right)\).
Find the gravitational potential at a point \(r=20\,\text{m}\) from a mass \(M=10\,\text{kg}\): [Hint: \(V=-\dfrac{GM}{r}\)].
Compute the work done in moving a mass \(m=2\,\text{kg}\) from \(r_1=4\,\text{m}\) to \(r_2=2\,\text{m}\) around a mass \(M=10\,\text{kg}\): \(W=GMm\!\left(\dfrac{1}{r_2}-\dfrac{1}{r_1}\right)\).
A planet has \(M_p=M_E/8\) and \(R_p=R_E/2\). Find \(\dfrac{v_{\text{esc, p}}}{v_{\text{esc, E}}}\).