JEE Tricky MCQs โ Gravitation (20 Qs)
Careful with limiting cases, ratios, and sign conventions. Click โShow Answerโ to reveal.
Q1
If Earthโs radius is halved with mass unchanged, surface g becomes:
A) 2g
B) 4g
C) g/2
D) g/4
Answer: B) 4g. Since \(g=GM/R^2\Rightarrow g’ = GM/(R/2)^2 = 4g\).
Q2
Two bodies m and 2m dropped from same height (vacuum). Ratio of KE just before hitting ground:
A) 1 : 1
B) 1 : 2
C) 2 : 1
D) 4 : 1
Answer: B) 1:2. \(KE=mgh\) โ mass.
Q3
Escape speed from a planet is \(v\). Minimum circular-orbit speed near surface is:
A) \(v/\sqrt{2}\)
B) \(v/2\)
C) \(v/\sqrt{3}\)
D) \(\sqrt{2}v\)
Answer: A) \(v/\sqrt{2}\). \(v_e=\sqrt{2gR},\ v_o=\sqrt{gR}=v_e/\sqrt{2}\).
Q4
A satellite orbits just above Earth. If Earthโs radius increases (mass same), its orbital speed:
A) Increases
B) Decreases
C) Remains same
D) Becomes infinite
Answer: B) Decreases. \(v=\sqrt{GM/R}\).
Q5
If \(g_h = g/9\) at height \(h\), then \(h=\) ? (Take Earth radius \(R\))
A) \(2R\)
B) \(3R\)
C) \(8R\)
D) \(R\)
Answer: A) \(2R\). \(g_h/g=(R/(R+h))^2=1/9 \Rightarrow R+h=3R\Rightarrow h=2R\).
Q6
The gravitational field inside a uniform thin spherical shell is:
A) Constant and non-zero
B) Zero everywhere
C) Maximum at center
D) Decreases linearly with radius
Answer: B) Zero everywhere.
Q7
Approximate ratio \(v_{e,\text{Earth}}/v_{e,\text{Moon}}\) is:
A) 5.0
B) 2.38
C) 11.2
D) 0.5
Answer: A) ~5.0 (โ4.7 using 11.2 km/s and 2.38 km/s).
Q8
If a planetโs density doubles and its radius halves, surface \(g\) changes by factor:
A) 1
B) 2
C) 4
D) 8
Answer: A) 1. \(g\propto \rho R\Rightarrow 2\rho \cdot (R/2)=\rho R\).
Q9
A body weighs 60 N on Earth. On a planet of the same density but double Earthโs radius, its weight is:
A) 30 N
B) 60 N
C) 120 N
D) 240 N
Answer: C) 120 N. With same density, \(g\propto R\). Doubling \(R\Rightarrow g\) doubles.
Q10
Two circular orbits of radii \(r\) and \(4r\). The ratio \(v_{r}/v_{4r}\) is:
A) 1/2
B) 1
C) 2
D) 4
Answer: C) 2. \(v\propto 1/\sqrt{r}\Rightarrow \sqrt{4r/r}=2\).
Q11
In an elliptical orbit, if apogee distance is twice perigee distance (\(r_a=2r_p\)), then \(v_a/v_p\) equals:
A) 1/2
B) 1
C) 2
D) \(\sqrt{2}\)
Answer: A) 1/2. Angular momentum conservation \(r v_t=\text{const}\).
Q12
Minimum energy per unit mass to free a satellite from a circular orbit of radius \(r\) around Earth is:
A) \(GM/r\)
B) \(GM/2r\)
C) \(2GM/r\)
D) \(GM/4r\)
Answer: B) \(GM/2r\). Binding energy per unit mass in circular orbit.
Q13
At what height will weight reduce by 36%? (i.e., become 64% of surface value)
A) \(0.25R\)
B) \(0.36R\)
C) \(0.50R\)
D) \(R\)
Answer: A) \(0.25R\). \((R/(R+h))^2=0.64\Rightarrow R+h=1.25R\).
Q14
A projectile is fired vertically with speed equal to orbital speed \(v_o\). Max altitude attained is:
A) \(R/2\)
B) \(R\)
C) \(2R\)
D) Escapes
Answer: B) \(R\). Energy: \(E=\frac12 mv_o^2-\frac{GMm}{R}=-\frac{GMm}{2R}=-\frac{GMm}{R+h}\Rightarrow h=R\).
Q15
Near Earthโs surface, fractional decrease of \(g\) per km of altitude is closest to:
A) 0.003%
B) 0.03%
C) 0.3%
D) 3%
Answer: B) ~0.03%. \(\Delta g/g\approx 2h/R \approx 2\times10^3/6.37\times10^6\approx3.1\times10^{-4}\).
Q16
Time period of oscillation through a diameter tunnel (uniform Earth) compared to low Earth circular orbit period is:
A) Smaller
B) Larger
C) Equal
D) Not comparable
Answer: C) Equal. Both \(T=2\pi\sqrt{R/g}\) (~84.4 min).
Q17
A planet has the same mass as Earth but thrice the radius. Its escape speed (vs Earthโs) is:
A) Same
B) 3 times
C) 1/3 times
D) \(1/\sqrt{3}\) times
Answer: D) \(1/\sqrt{3}\). \(v_e\propto\sqrt{M/R}\).
Q18
Two masses attract with force \(F\). If separation increases by 1%, force becomes approximately:
A) \(F(1+1\%)\)
B) \(F(1-1\%)\)
C) \(F(1-2\%)\)
D) \(F(1-4\%)\)
Answer: C) \(F(1-2\%)\). \(F\propto r^{-2}\Rightarrow dF/F \approx -2\,dr/r\).
Q19
If Earth suddenly stopped rotating, a personโs weight at the equator would:
A) Decrease by ~0.35%
B) Increase by ~0.35%
C) Increase by ~3.5%
D) Remain same
Answer: B) Increase by ~0.35%. Loss of centrifugal reduction \( \omega^2R \approx 0.034 \, \mathrm{m\,s^{-2}}\).
Q20
To escape Earth with residual speed \(u\) at infinity, the required launch speed from the surface is:
A) \(v_e – u\)
B) \(v_e + u\)
C) \(\sqrt{v_e^2 + u^2}\)
D) \(\sqrt{v_e^2 – u^2}\)
Answer: C) \(\sqrt{v_e^2 + u^2}\). From energy: \(\tfrac12 v_0^2 – GM/R = \tfrac12 u^2\).
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