TS EAMCET · Physics · Motion In Two Dimensions
Consider a wheel rotating around a fixed axis. If the rotation angle \(\theta\) varies with time as \(\theta=a t^2\), then the total acceleration of a point \(A\) on the rim of the wheel is \((v\) being the tangential velocity)
- A \(\frac{v}{t} \sqrt{1+4 a^2 t^4}\)
- B \(\frac{v}{t}\)
- C \(\frac{v}{t}\left(1+4 a^2 t^4\right)\)
- D \(\sqrt{\left(1+4 a^2 t^4\right)}\)
Answer & Solution
Correct Answer
(A) \(\frac{v}{t} \sqrt{1+4 a^2 t^4}\)
Step-by-step Solution
Detailed explanation
Given, \(\theta=a t^2\) So, angular velocity, \(\omega=\frac{d \theta}{d t}=2 a t\) Linear tangential velocity, \[ v=\omega r \quad=2 a t r \quad \frac{v}{t}=2 a r \] So, tangential linear acceleration of particle is \[ a_t=\frac{d v}{d t}=2 a r \] and angular acceleration of…
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
- Moment of inertia of a body about an axis is \(4 \mathrm{~kg}-\mathrm{m}^2\). The body is initially at rest and a torque of \(8 \mathrm{~N}\)-m starts acting on it along the same axis. Work done by the torque in \(20 \mathrm{~s}\), in joules, isTS EAMCET 2013 Medium
- A transverse wave propagating on a stretched string of linear density \(3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}\) is represented by the equation \(y=0.2 \sin (15 x+60 t)\) where \(x\) is in metres and \(t\) is in seconds. The tension in the string (in newton) isTS EAMCET 2005 Hard
- The displacement of a particle is given by the relation \(x=4(\cos \pi t+\sin \pi t)\). The amplitude of the particle isTS EAMCET 2023 Medium
- An object of mass \(2 m\) is projected with a speed of \(100 \mathrm{~ms}^{-1}\) at an angle \(\theta=\sin ^{-1}\left(\frac{3}{5}\right)\) to the horizontal. At the highest point, the object breaks into two pieces of same mass \(m\) and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in metre) is (Given, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )TS EAMCET 2007 Hard
- A planet of mass \(m\) moves around the Sun along an elliptical path with a period of revolution \(T\). During the motion, the planet's maximum and minimum distance from Sun is \(R\) and \(\frac{R}{3}\) respectively. If \(T^2=\alpha R^3\), then the magnitude of constant \(\alpha\) will beTS EAMCET 2019 Medium
- A steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is \(B\). If the same wire is bent into a circular loop of \(n\) turns, the magnetic field at the centre of the coil isTS EAMCET 2014 Medium
More PYQs from TS EAMCET
- A square loop of side ' \(a\) ' and carrying a current ' \(\mathrm{T}\) ' is suspended from an insulting hanger of a spring balance as shown in the figure. The transverse magnetic field ' \(\mathrm{B}\) ' directed into the paper occurs only at the bottom side of the loop. When direction of current in the loop is reversed, the change in the reading of spring balance is
TS EAMCET 2023 Easy - The initial and final velocities of a body projected vertically from the ground are \(20 \mathrm{~ms}^{-1}\) and \(18 \mathrm{~ms}^{-1}\) respectively. The maximum height reached by the body is (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )TS EAMCET 2025 Easy
- An ideal gas goes through a process \(A \rightarrow B \rightarrow C \rightarrow A\) cycle. The process, \(A \rightarrow B\) is adiabatic. Calculate the work done in the process \(A \rightarrow B\).
TS EAMCET 2021 Hard - Which of the following statements is NOT true?TS EAMCET 2022 Easy
- A particle of charge \(q\), mass \(m\) and energy \(E\) has de-Broglie wavelength \(\lambda\). For a particle of charge \(2 q\), mass \(2 m\) and energy \(2 E\), the de-Broglie wavelength isTS EAMCET 2019 Easy
- A bar-magnet of moment of inertia \(49 \times 10^{-2} \mathrm{~kg}-\mathrm{m}^2\) vibrates in a magnetic field of induction \(0.5 \times 10^{-4} \mathrm{~T}\). The time period of vibration is \(8.8 \mathrm{~s}\). The magnetic moment of the bar magnet isTS EAMCET 2007 Medium