JEE Mains · Physics · STD 11 - 3.2 motion in plane
A car is moving on a circular path of radius \(600\,m\) such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of \(54\,km / hr\) is \(t \left(1- e ^{-\pi / 2}\right)\,s\). The value of \(t\) is \(.............\).
- A \(20\)
- B \(40\)
- C \(10\)
- D \(15\)
Answer & Solution
Correct Answer
(B) \(40\)
Step-by-step Solution
Detailed explanation
\(v \frac{ dv }{ dx }=\frac{ v ^2}{ R } \Rightarrow \int \limits_{15}^{ v } \frac{ dv }{ v }=\frac{1}{ R } \int \limits_0^{ x } dx\) \(v =15 e ^{ x / R }\) \(\frac{ dx }{ dt }=15 e ^{ x / R }\) \(\frac{\pi R }{2} \int \limits_0^2 e ^{- x / R } dx =15 \int \limits_0^{t_0} dt\)…
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
- Given below are two statements. Statement \(I\) : Electric potential is constant within and at the surface of each conductor. Statement \(II\) : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options give below.JEE Mains 2022 Medium
- Match the LIST-I with LIST-II
Choose the correct answer from the options given below :LIST-I LIST-II (A) Gravitational constant (I) \(\left[\mathrm{LT}^{-2}\right]\) (B) Gravitational potential energy (II) \(\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]\) (C) Gravitational potential (III) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\) (D) Acceleration due to gravity (IV) \(\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\) JEE Mains 2025 Medium - A hypothetical gas expands adiabatically such that its volume changes from \(8\) litres to \(27\) litres. If the ratio of final pressure of the gas to initial pressure of the gas is \(\frac{16}{81}\). Then the ratio of \(\frac{C_P}{C_V}\) will beJEE Mains 2023 Medium
- For the given circuit the current \(i\) through the battery when the key in closed and the steady state has been reached is .....\(A\)
JEE Mains 2021 Hard - A uniform disc of radius \(R\) and mass \(M\) is free to rotate only about its axis. A string is wrapped over its rim and a body of mass \(m\) is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is
JEE Mains 2017 Hard - Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip
JEE Mains 2014 Hard
More PYQs from JEE Mains
- The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\)JEE Mains 2022 Medium
- If the mean of the data : \(7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8\) is \(8\), then the variance of this data isJEE Mains 2018 Hard
- A granite rod of \(60\ cm\) length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is \(2.7 \times 10^3 \) \(kg/m^3\) and its Young's modulus is \(9.27 \times 10^{10}\) \(Pa\) What will be the fundamental frequency of the longitudinal vibrations .... \(kHz\) ?JEE Mains 2018 Hard
- The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as \(R_1\) has the colour code (Orange, Red, Brown). The resistors \(R_2\) and \(R_4\) are \(80\, \Omega \) and \(40\,\Omega \), respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as \(R_3\) would be
JEE Mains 2019 Hard - Match List \(I\) with List \(II.\)
Choose the correct answer from the options given below:List \(I\) List \(II\) \((a)\) Rectifier \((i)\) Used either for stepping up or stepping down the \(a.c.\) voltage \((b)\) Stabilizer \((ii)\) Used to convert \(a.c.\) voltage into \(d.c.\) voltage \((c)\) Transformer \((iii)\) Used to remove any ripple in the rectified output voltage \((d)\) Filter \((iv)\) Used for constant output voltage even when the input voltage or load current change JEE Mains 2021 Medium - Let \(S\) be the set of all values of \(\lambda\), for which the shortest distance between the lines \(\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{z+6}{1}\) and \(\frac{x+\lambda}{3}=\frac{y}{-4}=\frac{z-6}{0}\) is \(13\) Then \(8\left|\sum_{\lambda \in S} \lambda\right|\) is equal toJEE Mains 2023 Medium