Physics || JEE Main previous year questions with Solutions

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Topic Question Set

Q 1 :
If a rubber ball falls from a height $h$ and rebounds up to the height of $h / 2$ . The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are [2024]

$40 %, \sqrt{2 g h}$
$50 %, \sqrt{\frac{g h}{2}}$
$50 %, \sqrt{2 g h}$
$50 %, \sqrt{g h}$

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(C) Velocity just before collision = $\sqrt{2 g h}$

Velocity just after collision = $\sqrt{2 g (\frac{h}{2})}$

$∴$ $∆ K E = \frac{1}{2} m (2 g h) - \frac{1}{2} m g h = \frac{1}{2} m g h$

$∴$ % loss in energy $\frac{∆ K E}{K E_{i}} \times 100$

$\Rightarrow \frac{∆ K E}{K E_{i}} \times 100 = \frac{\frac{1}{2} m g h}{\frac{1}{2} m g 2 h} \times 100 = 50 %$

Q 2 :
A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by (given $g = 9.8$ $m / s^{2}$ ) [2024]

4.32 kg ${ms}^{- 1}$
43.2 kg ${ms}^{- 1}$
23.9 kg ${ms}^{- 1}$
2.39 kg ${ms}^{- 1}$

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(4)

$m = 100 g = 0.1 kg, h_{1} = 10 m, h_{2} = 5 m$

$u = \sqrt{2 g h_{1}} = \sqrt{2 \times 98} m/s$

$v = \sqrt{2 g h_{2}} = \sqrt{98} m/s$

Impulse $= Δ \vec{P} = {\vec{P}}_{f} - {\vec{P}}_{i}$

$= 0.1 [\sqrt{98} + \sqrt{2 \times 98}]$

$\approx 2.39 kg m/s$

Q 3 :
A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10^{- 2}$ kg moving with a speed of $2 \times 10^{2}$ ${ms}^{- 1}$ . The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10$ $m / s^{2}$ ) [2024]

0.30 m
0.20 m
0.35 m
0.40 m

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(2)

$P_{i} = P_{f} \Rightarrow m u = (M + m) V$

$m u = (M + m) V$

$10^{- 2} \times 2 \times 10^{2} ≅ 1 \times V \Rightarrow V ≅ 2 m/s$

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