JEE Mains · Physics · STD 11 - 4.1 newtons laws of motion
A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate \(\frac{ dM ( t )}{ dt }= bv ^{2}( t ),\) where \(v ( t )\) is its instantaneous velocity. The instantaneous acceleration of the satellite is
- A \(-\frac{2 b v^{3}}{M(t)}\)
- B \(-\frac{ bv ^{3}}{2 M ( t )}\)
- C \(-b v^{3}(t)\)
- D \(-\frac{b v^{3}}{M(t)}\)
Answer & Solution
Correct Answer
(D) \(-\frac{b v^{3}}{M(t)}\)
Step-by-step Solution
Detailed explanation
\(\frac{\operatorname{dm}( t )}{ dt }= bv ^{2}\) \(F _{\text {thast }}= v \frac{ dm }{ dt }\) Force on statellile \(=-\overrightarrow{ v } \frac{ dm ( t )}{ dt }\) \(M ( t ) a =- v \left( bv ^{2}\right)\) \(a = - \frac{ bv ^{3}}{ M ( t )}\)
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 mixture of \(2\, moles\) of helium gas (atomic mass \(= 4\, u\)), and \(1\, mole\) of argon gas (atomic mass \(= 40\, u\)) is kept at \(300\, K\) in a container. The ratio of their rms speeds \(\left[ {\frac{{{V_{rms}}{\rm{(helium)}}}}{{{V_{rms}}{\rm{(argon)}}}}} \right]\), is close toJEE Mains 2019 Medium
- Given below are two statements: Statement \(I :\) An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement \(II :\) If \(R\) is the radius of a solid metallic sphere and \(Q\) be the total charge on it. The electric field at any point on the spherical surface of radius \(r ( < R )\) is zero but the electric flux passing through this closed spherical surface of radius \(r\) is not zero. In the light of the above statements, choose the correct answer from the options given below:JEE Mains 2021 Hard
- An \(npn\) transistor operates as a common emitter amplifier, with a power gain of \(60\, dB\). The input circuit resistance Is \(100\,\Omega \) and the output load resistance is \(10 \,k\,\Omega \). the common emitter current gain \(\beta \) isJEE Mains 2019 Hard
- A copper ball of radius \(1\, cm\) and work function \(4.47\,eV\) is irradiated with ultraviolet radiation of wavelength \(2500\mathop A\limits^o \). The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball isJEE Mains 2013 Hard
- A tuning fork \(A\) of unknown frequency produces \(5\, beats/s\) with a fork of known frequency \(340\, Hz\). When fork \(A\) is filed, the beat frequency decreases to \(2\, beats/s.\) What is the frequency of fork \(A\) ? (in \(Hz\))JEE Mains 2021 Hard
- An electric field \(\vec E\, = (25 \hat i + 30 \hat j)\,NC^{-1}\) exists in a region of space. If the potential at the origin is taken to be zero then the potential at \(x\, = 2\, m, y\, = 2\, m\) is......\(volt\)JEE Mains 2015 Medium
More PYQs from JEE Mains
- Let \(y = y(x)\) be the solution curve of the differential equation \((1 + \sin x)\dfrac{dy}{dx} + (y+1)\cos x = 0\), \(y(0) = 0\). If the curve \(y = y(x)\) passes through the point \(\left(\alpha, \dfrac{-1}{2}\right)\), then a value of \(\alpha\) is :JEE Mains 2026 Easy
- In a Young double slit experiment, the wavelength of incident light is \(6000\) Å, the separation between slits \(S_1\) and \(S_2\) is \(5\) cm and the distance between slits plane and screen is \(50\) cm, as shown in the figure below. If the resultant intensity at \(P\) is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å.
JEE Mains 2026 Hard - The shortest distance between the line \(\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5} \text { and } \frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}\) is :JEE Mains 2024 Medium
- A bullet of \('4\,g'\) mass is fired from a gun of mass \(4 \,{kg}\). If the bullet moves with the muzzle speed of \(50\, {ms}^{-1}\), the impulse imparted to the gun and velocity of recoil of gun are :JEE Mains 2021 Medium
- If \(I _{ n }=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cot ^{ n } x dx ,\) then :JEE Mains 2021 Hard
- A value of \(x\) satisfying the equation \(\sin \left[ {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right] = \cos \left[ {{{\tan }^{ - 1}}\,x} \right]\) , isJEE Mains 2017 Hard