JEE Mains · Physics · STD 11 - 7. gravitation
At a certain depth "\(d\)" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height \(3\,R\) above earth surface. Where \(R\) is Radius of earth (Take \(R =6400\,km\) ). The depth \(d\) is equal to \(............\,km\)
- A \(5260\)
- B \(640\)
- C \(2560\)
- D \(4800\)
Answer & Solution
Correct Answer
(D) \(4800\)
Step-by-step Solution
Detailed explanation
\(\frac{ GM }{ R ^2}\left[1-\frac{ d }{ R }\right]=\frac{4 \times GM }{(4 R )^2}\) \(1-\frac{ d }{ R }=\frac{1}{4} \Rightarrow \frac{ d }{ R }=\frac{3}{4} \Rightarrow d \frac{3}{4} R\) \(d =4800\,km\)
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 particle is moving along a circular path with a constant speed of \(10\,ms^{-1}.\) What is the magnitude of the change in velocity of the particle, when it moves through an angle of \(60^{o}\) around the centre of the circle .......... \(m/s\)JEE Mains 2019 Medium
- A capacitor of capacitance \(C=1\, \mu \,{F}\) is suddenly connected to a battery of \(100\, volt\) through a resistance \({R}=100\, \Omega\). The time taken for the capacitor to be charged to get \(50 \,{V}\) is \(....\,\times \,10^{-4}\,s.\) [Take \(\ln 2=0.69]\)
JEE Mains 2021 Medium - A particle is executing simple harmonic motion. Its amplitude is \(A\) and time period is \(5\) sec. The time required by it to move from \(x = A\) to \(x = \dfrac{A}{\sqrt{2}}\) is _______ sec.JEE Mains 2026 Medium
- The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are
JEE Mains 2020 Medium - During the propagation of electromagnetic waves in a mediumJEE Mains 2014 Easy
- In an alpha particle scattering experiment distance of closest approach for the \(\alpha\) particle is \(4.5 \times 10^{-14} \mathrm{~m}\). If target nucleus has atomic number \(80\) , then maximum velocity of \(\alpha\)-particle is _______ \(\times 10^5\) \(\mathrm{m} / \mathrm{s}\) approximately. \(\left(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}\right.\) unit, mass of \(\alpha\) particle \(=\) \(\left.6.72 \times 10^{-27} \mathrm{~kg}\right)\)JEE Mains 2024 Hard
More PYQs from JEE Mains
- The elastic potential energy stored in a steel wire of length \(20\,m\) stretched through \(2 \,cm\) is \(80\,J\). The cross sectional area of the wire is \(.........\,mm ^2\) (Given, \(y =2.0 \times 10^{11}\,Nm ^{-2}\) )JEE Mains 2023 Medium
- Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.
JEE Mains 2024 Hard - Let \(f ( x )=\sum \limits_{ k =1}^{10} kx ^{ k }, x \in R\). If \(2 f(2)+f^{\prime}(2)=119(2)^{ n }+1\) then \(n\) is equal to \(..........\).JEE Mains 2023 Hard
- A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is ___________ mV.JEE Mains 2026 Medium
- An air bubble of volume \(1\,cm ^3\) rises from the bottom of a lake \(40\,m\) deep to the surface at a temperature of \(12^{\circ}\,C\). The atmospheric pressure is \(1 \times 10^5 Pa\), the density of water is \(1000\,kg / m ^3\) and \(g =10\,m / s ^2\). There is no difference of the temperature of water at the depth of \(40\,m\) and on the surface. The volume of air bubble when it reaches the surface will be \(..........\,cm^{3}\)JEE Mains 2023 Medium
- Let the line \(\frac{x}{1}=\frac{6-y}{2}=\frac{z+8}{5}\) intersect the lines \(\frac{x-5}{4}=\frac{y-7}{3}=\frac{z+2}{1}\) and \(\frac{x+3}{6}=\frac{3-y}{3}=\frac{z-6}{1}\) at the points \(A\) and \(B\) respectively. Then the distance of the mid-point of the line segment \(A B\) from the plane \(2 x-2 y+z=14\) isJEE Mains 2023 Hard