Question

The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass $4 \mathrm{k}\mathrm{g}$. (The coordinates of the same are shown in the figure) are:

JEE Main 2020 (08 Jan Shift 1)

Options

• A: $\left(\mathrm{1.25 }\mathrm{m},\mathrm{}\mathrm{1.50 }\mathrm{}\mathrm{m}\right)$
• B: $\left(\mathrm{0.75 }\mathrm{m},\mathrm{}\mathrm{1.75 }\mathrm{}\mathrm{m}\right)$
• C: $\left(\mathrm{0.75 }\mathrm{m},\mathrm{}\mathrm{0.75 }\mathrm{}\mathrm{m}\right)$
• D: $\left(\mathrm{1 }\mathrm{m},\mathrm{}\mathrm{1.75 }\mathrm{}\mathrm{m}\right)$

Question

As shown in figure. When a spherical cavity (centred at $O$ ) of radius $1$ is cut out of a uniform sphere of radius $R$ (centred at $C$ ), the centre of mass of remaining (shaded part of sphere is at $G,$ i.e., on the surface of the cavity. $R$ can be determined by the equation:

JEE Main 2020 (08 Jan Shift 2)

Options

• A: $\left(R^2+R+1\right)\left(2-R\right)=1$
• B: $\left(R^2-R-1\right)\left(2-R\right)=1$
• C: $\left(R^2-R+1\right)\left(2-R\right)=1$
• D: $\left(R^2+R-1\right)\left(2-R\right)=1$

Question

A particle of mass m is projected with a speed u from the ground at an angle $\theta =\frac{\pi }{3}$ w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\widehat{i}.$ The horizontal distance covered by the combined mass before reaching the ground is:

JEE Main 2020 (09 Jan Shift 2)

Options

• A: $\frac{3\sqrt{3}}{8}\frac{u^2}{g}$
• B: $\frac{3\sqrt{2}}{4}\frac{u^2}{g}$
• C: $\frac{5}{8}\frac{u^2}{g}$
• D: $2\sqrt{2}\frac{u^2}{g}$

Question

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A, B$ and $C$ are $m, 2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9 \mathrm{m} {\mathrm{s}}^{-1}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C.$ All motions occur along the same straight line. The final speed of $C$ is :

JEE Main 2021 (27 Jul Shift 1)

Options

• A: $6 \mathrm{m} {\mathrm{s}}^{-1}$
• B: $9 \mathrm{m} {\mathrm{s}}^{-1}$
• C: $4 \mathrm{m} {\mathrm{s}}^{-1}$
• D: $3 \mathrm{m} {\mathrm{s}}^{-1}$

Question

A ball of mass $10 \mathrm{kg}$ moving with a velocity $10\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ along the $x$ -axis, hits another ball of mass $20 \mathrm{kg}$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$ -axis with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}.$ The second piece starts moving at an angle of $30°$ with respect to the $x$ -axis. The velocity of the ball moving at $30°$ with $x$ -axis is $x \mathrm{m} {\mathrm{s}}^{-1}.$ The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is

JEE Main 2021 (18 Mar Shift 1)

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Question

Two blocks of masses $10 \mathrm{kg}$ and $30 \mathrm{kg}$ are placed on the same straight line with coordinates $\left(0,0\right)\mathrm{cm}$ and $\left(x,0\right)\mathrm{cm}$ respectively. The block of $10 \mathrm{kg}$ is moved on the same line through a distance of $6 \mathrm{cm}$ towards the other block. The distance through which the block of $30 \mathrm{kg}$ must be moved to keep the position of centre of mass of the system unchanged is

JEE Main 2022 (27 Jun Shift 1)

Options

• A: $4 \mathrm{cm}$ towards the $10 \mathrm{kg}$ block
• B: $2 \mathrm{cm}$ away from the $10 \mathrm{kg}$ block
• C: $2 \mathrm{cm}$ towards the $10 \mathrm{kg}$ block
• D: $4 \mathrm{cm}$ away from the $10 \mathrm{kg}$ block

Question

Two bodies are having kinetic energies in the ratio $16:9.$ If they have same linear momentum, the ratio of their masses respectively is:

JEE Main 2023 (13 Apr Shift 1)

Options

• A: $3:4$
• B: $9:16$
• C: $16:9$
• D: $4:3$

Question

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1:2^{1/3}$. Their respective speed have a ratio of $n:1$. The value of $n$ is_________

JEE Main 2023 (11 Apr Shift 2)

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Question

A uniform thin metal plate of mass $10 \mathrm{~kg}$ with dimensions is shown. The ratio of $\mathrm{x}$ and $\mathrm{y}$ coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is ________

JEE Main 2024 (08 Apr Shift 1)

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Question

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

JEE Main 2024 (30 Jan Shift 1)

Options

• A: $4.32 \mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$
• B: $43.2 \mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$
• C: $23.9 \mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$
• D: $2.39 \mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$

Question

A uniform rod $AB$ of mass $2 \mathrm{kg}$ and Length $30 \mathrm{cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2 \mathrm{N} \mathrm{s}$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi }{\mathrm{x}} \mathrm{s},$ where $x=$ ____.

JEE Main 2024 (01 Feb Shift 2)

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