KCET · Physics · Motion In One Dimension
An athlete runs along a circular track of diameter 80 m . The distance travelled and the magnitude of displacement of the athlete when he covers \(3 / 4\) th of the circle is (in m)
- A \(60 \pi, 40 \sqrt{2}\)
- B \(40 \pi, 60 \sqrt{2}\)
- C \(120 \pi, 80 \sqrt{2}\)
- D \(80 \pi, 120 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(60 \pi, 40 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Given, diameter, \(d=80 \mathrm{~m}\)
\(\therefore \quad r=40 \mathrm{~m}\)
Distance travelled after completion of \(\frac{3}{4}\) revolution
\(=\frac{3}{4} \times 2 \pi r=\frac{3 \pi}{2} \times 40=60 \pi \mathrm{~m}\)
Displacement \(=\sqrt{r^2+r^2}=r \sqrt{2}=40 \sqrt{2} \mathrm{~m}\)
\(\therefore \quad r=40 \mathrm{~m}\)
Distance travelled after completion of \(\frac{3}{4}\) revolution
\(=\frac{3}{4} \times 2 \pi r=\frac{3 \pi}{2} \times 40=60 \pi \mathrm{~m}\)
Displacement \(=\sqrt{r^2+r^2}=r \sqrt{2}=40 \sqrt{2} \mathrm{~m}\)
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
- The temperature of a gas contained in a closed vessel of constant volume increases by \(1^{\circ} \mathrm{C}\) when the pressure of the gas is increased by \(1 \%\). The initial temperature of the gas isKCET 2010 Easy
- A smooth chain of length \(2 \mathrm{~m}\) is kept on a table such that its length of \(60 \mathrm{~cm}\) hangs frecly from the edge of the table. The total mass of the chain is \(4 \mathrm{~kg}\). The work done in pulling the entire chain on the table is (Take, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )KCET 2022 Hard
- With reference to the figure shown below, match the following:
List-I List-II (a) Angle of reflection (i) \(60^\circ\) (b) Value of \(\alpha\) (ii) \(120^\circ\) (c) Angle of deviation (iii) \(30^\circ\) KCET 2026 Easy - Magnetic susceptibility of Mg at 300 K is \(1.2 \times 10^{-5}\). What is its susceptibility at \(200 \mathrm{~K} ?\)KCET 2024 Easy
- For a transistor, \(\beta=100\). The value of \(\alpha\) isKCET 2012 Easy
- 'Young's modulus' is defined as the ratio ofKCET 2017 Medium
More PYQs from KCET
- \(A B C\) is triangle, \(G\) is the centroid, \(D\) is the mid-point of \(B C\). If \(A=(2,3)\) and \(G=(7,5)\), then the point \(D\) isKCET 2007 Hard
- If ' \(x\) ' takes negative permissible value, then \(\sin ^{-1} \mathrm{x}\) is equal toKCET 2009 Hard
- For a reaction, the value of rate constant at \(300 \mathrm{~K}\) is \(6.0 \times 10^5 \mathrm{~s}^{-1}\). The value of Arrhenius factor \(A\) at infinitely high temperature isKCET 2023 Medium
- Match the following.
(A) VNTR p. Largest gene (B) Inrons and exons q. DNA fingerprinting (C) Dystrophin r. Bulk DNA (D) Satellite S. Splicing KCET 2015 Easy - A transformer works on the principle ofKCET 2011 Easy
- If \(\mathrm{x}=\mathrm{t}^{2}+2\) and \(\mathrm{y}=2 \mathrm{t}\) represent the parametric equation of the parabolaKCET 2012 Easy