TS EAMCET · Physics · Work Power Energy
Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?
- A Statements I, II, III are true
- B Statements I, III are true, but statement II is false
- C Statement I is true, but statements II and III are false
- D Statements I, II are true, but statement III is false
Answer & Solution
Correct Answer
(C) Statement I is true, but statements II and III are false
Step-by-step Solution
Detailed explanation
We have \[ \begin{aligned} & \mathrm{K} . \mathrm{E}=\frac{1}{2} \mathrm{mV}^2 \\ & \frac{\mathrm{d}}{\mathrm{dx}}(\mathrm{K} . \mathrm{E})=\frac{1}{2} \times \mathrm{m} \times 2 \mathrm{~V} \frac{\mathrm{dV}}{\mathrm{dx}} \end{aligned} \] Slope of \((\) K.E \(-\mathrm{x})\)…
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