JEE Mains · Physics · STD 11 - 7. gravitation
The energy required to take a satellite to a height \(‘h’\) above Earth surface (radius of Earth \(= 6.4 \times 10^3\,km\) ) is \(E_1\) and kinetic energy required for the satellite to be in a circular orbit at this height is \(E_2.\) The value of \(h\) for which \(E_1\) and \(E_2\) are equal is
- A \(1.6\times 10^3\,km\)
- B \(3.2\times 10^3\,km\)
- C \(6.4\times 10^3\,km\)
- D \(1.28\times 10^4\,km\)
Answer & Solution
Correct Answer
(B) \(3.2\times 10^3\,km\)
Step-by-step Solution
Detailed explanation
\({E_1} =-\frac{{GMm}}{{R + h}} - \left( { - \frac{{GMm}}{R}} \right)\) \({E_2} = \frac{1}{2}m{\left( {\sqrt {\frac{{GM}}{{R + h}}} } \right)^2} = \frac{{GMm}}{{2\left( {R + h} \right)}}\) \({E_1} = {E_2}\,\,;\,\,h = \frac{R}{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A fighter plane of length \(20\, m\), wing span (distance from tip of one wing to the tip of the other wing) of \(15\,m\) and height \(5\,m\) is lying towards east over Delhi. Its speed is \(240\, ms^{-1}\) . The earth's magnetic field over Delhi is \(5 \times 10^{-5}\,T\) with the declination angle \( \sim {0^o}\) and dip of \(\theta\) such that \(\sin \,\theta = \frac{2}{3}\). If the voltage developed is \(V_B\) between the lower and upper side of the plane and \(V_W\) between the tips of the wings then \(V_B\) and \(V_W\) are close toJEE Mains 2016 Hard
- The graph shows how the magnification \(m\) produced by a thin lens varies with image distance \(v\). What is the focal length of the lens used?
JEE Mains 2019 Medium - A particle moving in a circle of radius \(R\) with uniform speed takes time \(\mathrm{T}\) to complete one revolution. If this particle is projected with the same speed at an angle \(\theta\) to the horizontal, the maximum height attained by it is equal to \(4 R\). The angle of projection \(\theta\) is then given by _______.JEE Mains 2024 Hard
- Water droplets are coming from an open tap at particular rate. The spacing between a droplet observed at \(4^{{th}}\;second\) after its fall to the next droplet is \(34.3 \,{m}\). At what rate the droplets are coming from the tap ? (Take \(g=9.8\, {m} / {s}^{2}\))JEE Mains 2021 Hard
- A mirror is used to produce an image with magnification of \(\frac{1}{4}\). If the distance between object and its image is 40 cm , then the focal length of the mirror is ________JEE Mains 2025 Hard
- A beam of light travelling along \(X\)-axis is described by the electric field \(E _{ y }=900 \sin \omega( t - x / c )\). The ratio of electric force to magnetic force on a charge \(q\) moving along \(Y\)-axis with a speed of \(3 \times 10^{7}\,ms ^{-1}\) will be. [Given speed of light \(=3 \times 10^{8}\,ms ^{-1}\) ]JEE Mains 2022 Medium
More PYQs from JEE Mains
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{ dy }{ dx }+\left(\frac{2 x ^{2}+11 x +13}{ x ^{3}+6 x ^{2}+11 x +6}\right)\) \(y=\frac{(x+3)}{x+1}, x>-1\), which passes through the point \((0,1)\). Then \(y (1)\) is equal to.JEE Mains 2022 Hard
- The mean and variance of \(7\) observations are \(8\) and \(16\) respectively. If two observations are \(6\) and \(8 ,\) then the variance of the remaining \(5\) observations is:JEE Mains 2021 Medium
- In a triangle \(\mathrm{ABC}, \mathrm{BC}=7, \mathrm{AC}=8, \mathrm{AB}=\alpha \in \mathrm{N}\) and \(\cos A=\frac{2}{3}\). If \(49 \cos (3 C)+42=\frac{m}{n}\), where \(\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\), then \(\mathrm{m}+\mathrm{n}\) is equal to ..........JEE Mains 2024 Hard
- If \(m\) is a non-zero number and \(\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x=f(x)+c\) , then \(f(x)\) isJEE Mains 2014 Hard
- If \(y \frac{d y}{d x}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right], x>0, \phi>0\), and \(y(1)=-1\) then \(\phi\left(\frac{\mathrm{y}^{2}}{4}\right)\) is equal to :JEE Mains 2021 Hard
- A random variable X takes values 0, 1, 2, 3 with probabilities \( \frac{2a+1}{30},\frac{8a-1}{30},\frac{4a+1}{30} \), b respectively, where \( a, b\in R \). Let μ and σ respectively be the mean and standard deviation of X such that \( \sigma^{2}+\mu^{2}=2 \). Then \( \frac{a}{b} \) is equal to :JEE Mains 2026 Hard