AP EAMCET · PHYSICS · Work Power Energy
A block of mass \(2 \mathrm{~kg}\) is initially at rest on a horizontal frictionless surface. A horizontal force \(\overrightarrow{\mathbf{F}}=\left(9-x^2\right) \hat{\mathbf{i}}\) newtons acts on it, when the block is at \(x=0\). The maximum kinetic energy of the block between \(x=0\) and \(x=3 \mathrm{~m}\) in joule is
- A \(24\)
- B \(20\)
- C \(18\)
- D \(15\)
Answer & Solution
Correct Answer
(C) \(18\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{KE}=\int F d x \\ & \qquad \begin{aligned} \mathrm{KE} & =\int_{x=0}^{x=3}\left(9-x^2\right) d x \\ & =9 \int_{x=0}^{x=3} d x-\int_{x=0}^{x=3} x^2 d x \\ & =9[x]_0^3-\left[\frac{x^3}{3}\right]_0^3=27-9=18 \mathrm{~J} .\end{aligned}\end{aligned}\)
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 force per unit length on a straight wire carrying current of 8 A making an angle of \(30^{\circ}\) with a uniform magnetic field of 0.15 T isAP EAMCET 2025 Easy
- A particle undergoing simple harmonic motion has an amplitude of \(10 \mathrm{~cm}\). When the particle is at a displacement of \(6 \mathrm{~cm}\) from the centre, then the ratio of its kinetic energy to potential energy isAP EAMCET 2022 Easy
- A Carnot engine operating between temperatures \(600 \mathrm{~K}\) and \(300 \mathrm{~K}\), absorbs \(800 \mathrm{~J}\) of heat from the source. The mechanical work done per cycle isAP EAMCET 2022 Easy
- A man pushes the wall and fails to displace it. He doesAP EAMCET 2020 Easy
- Six point charges each of the magnitude \(Q\) are placed at the vertices of a regular hexagon of side \(a\) as shown in the figure. Electric field intensity on the line passing through the centre \(O\) and perpendicular to the plane of the figure at a large distance \(x(\gg > a)\) from \(O\) is
\(\left(\text {Let, } \frac{1}{4 \pi \in_0}=k\right)\)
AP EAMCET 2019 Hard - Ball \(A\) of mass \(1 \mathrm{~kg}\) moving along a straight line with a velocity of \(4 \mathrm{~ms}^{-1}\) hits another ball \(B\) of mass \(3 \mathrm{~kg}\) which is at rest. After collision, they stick together and move with the same velocity along the same straight line. If the time of impact of the collision is \(0.1 \mathrm{~s}\) then the force exerted on \(B\) isAP EAMCET 2022 Hard
More PYQs from AP EAMCET
- Assertion: Transition metals and their complexes show catalytic activity. Reason: The activation energy of a reaction is lowered by the catalyst.AP EAMCET 2022 Easy
- Three charges \(\mathrm{Q},+\mathrm{q}\) and \(+\mathrm{q}\) are placed at the vertices of a right angled isoscels triangle as shown in the figure. If the net electrostatic potential energy of the system is zero, the value of \(Q\) is
AP EAMCET 2017 Medium - If the direction cosines of two lines are given by \(l+m+n=0\) and \(l^2-5 m^2+n^2=0\), then the angle between them isAP EAMCET 2014 Medium
- If \(x=\frac{2}{5}+\frac{1 \cdot 3}{2 !}\left(\frac{2}{5}\right)^2+\frac{1 \cdot 3 \cdot 5}{3 !}\left(\frac{2}{5}\right)^3+\ldots\), then \(x+\frac{1}{x}=\)AP EAMCET 2019 Medium
- Match the following
The correct answer isAP EAMCET 2024 Easy - Two charges and are placed at points A and B separated by a distance of . Find the electric field at a point P on the perpendicular bisector of A B, at a distance of from its mid-point.
AP EAMCET 2021 Medium