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JEE Main 2021 (Online) 31st August Evening Shift

Numerical
A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The acceleration of the particle is ___________ m/s2.

Explanation

y = mx + C

v2 = $${{20} \over {10}}$$x + 20

v2 = 2x + 20

2v$${{dv} \over {dx}}$$ = 2

$$\therefore$$ a = v$${{dv} \over {dx}}$$ = 1
2

JEE Main 2021 (Online) 27th August Morning Shift

Numerical
If the velocity of a body related to displacement x is given by $$\upsilon = \sqrt {5000 + 24x}$$ m/s, then the acceleration of the body is .................... m/s2.

Explanation

$$V = \sqrt {5000 + 24x}$$

$${{dV} \over {dx}} = {1 \over {2\sqrt {5000 + 24x} }} \times 24 = {{12} \over {\sqrt {5000 + 24x} }}$$

Now, $$a = V{{dV} \over {dx}}$$

$$= \sqrt {5000 + 24x} \times {{12} \over {\sqrt {5000 + 24x} }}$$

a = 12 m/s2
3

JEE Main 2021 (Online) 26th August Morning Shift

Numerical
Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same initial velocity of 35 m/s, then these balls collide at a height of ............... m. (Take g = 10 m/s2)

Explanation

Image

When both balls will collied

y1 = y2

$$35t - {1 \over 2} \times 10 \times {t^2} = 35(t - 3) - {1 \over 2} \times 10 \times {(t - 3)^2}$$

$$35t - {1 \over 2} \times 10 \times {t^2} = 35t - 105 - {1 \over 2} \times 10 \times {t^2} - {1 \over 2} \times 10 \times {3^2} + {1 \over 2} \times 10 \times 6t$$

0 = 150 $$-$$ 30 t

t = 5 sec

$$\therefore$$ Height at which both balls will collied

$$h = 35t - {1 \over 2} \times 10 \times {t^2}$$

$$= 35 \times 5 - {1 \over 2} \times 10 \times {5^2}$$

h = 50 m
4

JEE Main 2021 (Online) 27th July Evening Shift

Numerical
A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$$^\circ$$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $$\theta$$ with the line AB should be _________$$^\circ$$, so that the swimmer reaches point B.

Explanation

Both velocity vectors are of same magnitude therefore resultant would pass exactly midway through them

$$\theta$$ = 30$$^\circ$$

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