Question

A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v.$ If the coefficient of static friction between the tyres and the track is ${\mu }_{\mathrm{s}},$ then the magnitude of negative lift $F_L$ acting downwards on the car is:

JEE Main 2021 (17 Mar Shift 1)

Options

• A: $m\left(\frac{v^2}{{\mu }_{s}R}+g\right)$
• B: $m\left(\frac{v^2}{{\mu }_{s}R}-g\right)$
• C: $m\left(g-\frac{v^2}{{\mu }_{s}R}\right)$
• D: $-m\left(g+\frac{v^2}{{\mu }_{s}R}\right)$

Question

A particle is projected with velocity $v_0$ along $x$-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. $ma=-\alpha x^2.$ The distance at which the particle stops:

JEE Main 2021 (24 Feb Shift 2)

Options

• A: ${\left(\frac{2v_0}{3\alpha }\right)}^{\frac{1}{3}}$
• B: ${\left(\frac{3m{v}_0^2}{2\alpha }\right)}^{\frac{1}{3}}$
• C: ${\left(\frac{3v_0^2}{2\alpha }\right)}^{\frac{1}{2}}$
• D: ${\left(\frac{2v_0^2}{3\alpha }\right)}^{\frac{1}{2}}$

Question

A swimmer can swim with velocity of $12 \mathrm{km}/\mathrm{h}$ in still water. Water flowing in a river has velocity $6 \mathrm{km}/\mathrm{h}$. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________$°$. 

(Round off to the Nearest Integer) (find the angle in degree)

JEE Main 2021 (16 Mar Shift 2)

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Question

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

JEE Main 2021 (27 Jul Shift 2)

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Question

A projectile is launched at an angle $\alpha$ with the horizontal with a velocity $20{ \mathrm{m} \mathrm{s}}^{-1}$. After $10 \mathrm{s}$, its inclination with horizontal is $\beta$. The value of $\tan \beta$ will be : $\left(g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$.

JEE Main 2022 (27 Jun Shift 1)

Options

• A: $\tan \alpha +5\sec \alpha$
• B: $\tan \alpha -5\sec \alpha$
• C: $2\tan \alpha -5\sec \alpha$
• D: $2\tan \alpha +5\sec \alpha$

Question

A girl standing on road holds her umbrella at $45°$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2} \mathrm{km} {\mathrm{h}}^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is

JEE Main 2022 (27 Jun Shift 1)

Options

• A: $30 \mathrm{km} {\mathrm{h}}^{-1}$
• B: $\frac{25}{\sqrt{2}} \mathrm{km} {\mathrm{h}}^{-1}$
• C: $\frac{30}{\sqrt{2}} \mathrm{km} {\mathrm{h}}^{-1}$
• D: $25 \mathrm{km} {\mathrm{h}}^{-1}$

Question

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y=5x\left(1-x\right)$. The $y$ component vector of the initial velocity is _____  $\hat{j}$

(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

JEE Main 2022 (26 Jul Shift 1)

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Question

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____  degree.

JEE Main 2022 (29 Jul Shift 1)

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Question

The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$. Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be.

JEE Main 2023 (08 Apr Shift 2)

Options

• A: $200 \mathrm{m}$
• B: $10 \mathrm{m}$
• C: $5 \mathrm{m}$
• D: $10\sqrt{2} \mathrm{m}$

Question

A disc is rolling without slipping on a surface. The radius of the disc is $R.$ At $t=0,$ the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is

JEE Main 2023 (13 Apr Shift 1)

Options

• A: $2R$
• B: $R\sqrt{\left({\pi }^2+4\right)}$
• C: $\mathrm{R}\sqrt{\left({\pi }^2+1\right)}$
• D: $2R\sqrt{\left(1+4{\pi }^2\right)}$