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Mechanics — JEE Physics MCQs

Master Mechanics for JEE Main with free physics MCQs. Each question includes a detailed solution and instant feedback — practice at easy, medium, and hard difficulty levels to build exam-ready confidence.

8 practice questions with instant feedback and solutions.

Hard•Mechanics
A uniform wooden stick of mass 1.6 kg1.6 \mathrm{~kg} and length ll rests in an inclined manner on a smooth, vertical wall of height h(<l)h(<l) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 30∘30^{\circ} with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio h/lh / l and the frictional force ff at the bottom of the stick are (g=10 ms s2)\left(g=10 \mathrm{~ms} \mathrm{~s}^{2}\right)
Hard•Mechanics
A bar of mass M=1.00 kgM=1.00 \mathrm{~kg} and length L=0.20 mL=0.20 \mathrm{~m} is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass m=0.10 kgm=0.10 \mathrm{~kg} is moving on the same horizontal surface with 5.00 m s−15.00 \mathrm{~m} \mathrm{~s}^{-1} speed on a path perpendicular to the bar. It hits the bar at a distance L/2L / 2 from the pivoted end and returns back on the same path with speed v\mathrm{v}. After this elastic collision, the bar rotates with an angular velocity ω\omega. Which of the following statement is correct?
Hard•Mechanics
A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3×1053 \times 10^{5} times heavier than the Earth and is at a distance 2.5×1042.5 \times 10^{4} times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is ve=11.2 km s−1v_{e}=11.2 \mathrm{~km} \mathrm{~s}^{-1}. The minimum initial velocity (vS)\left(v_{S}\right) required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet) [A]vS=22 km s−1[\mathrm{A}] \quad v_{S}=22 \mathrm{~km} \mathrm{~s}^{-1} [B]vS=42 km s−1[\mathrm{B}] v_{S}=42 \mathrm{~km} \mathrm{~s}^{-1} [C]vS=62 km s−1[\mathrm{C}] \quad v_{S}=62 \mathrm{~km} \mathrm{~s}^{-1} D. vS=72 km s−1v_{S}=72 \mathrm{~km} \mathrm{~s}^{-1}
Medium•Mechanics
Consider an expanding sphere of instantaneous radius RR whose total mass remains constant. The expansion is such that the instantaneous density ρ\rho remains uniform throughout the volume. The rate of fractional change in density (1ρdρdt)\left(\frac{1}{\rho} \frac{d \rho}{d t}\right) is constant. The velocity vv of any point on the surface of the expanding sphere is proportional to
Medium•Mechanics
Consider a spherical gaseous cloud of mass density ρ(r)\rho(r) in free space where rr is the radial distance from its center. The gaseous cloud is made of particles of equal mass mm moving in circular orbits about the common center with the same kinetic energy KK. The force acting on the particles is their mutual gravitational force. If ρ(r)\rho(r) is constant in time, the particle number density n(r)=ρ(r)/mn(r)=\rho(r) / m is [ GG is universal gravitational constant]
Medium•Mechanics
Two satellites P\mathrm{P} and Q\mathrm{Q} are moving in different circular orbits around the Earth (radius RR ). The heights of P\mathrm{P} and Q\mathrm{Q} from the Earth surface are hPh_{\mathrm{P}} and hQh_{\mathrm{Q}}, respectively, where hP=R/3h_{\mathrm{P}}=R / 3. The accelerations of P\mathrm{P} and Q\mathrm{Q} due to Earth's gravity are gPg_{\mathrm{P}} and gQg_{\mathrm{Q}}, respectively. If gP/gQ=36/25g_{\mathrm{P}} / g_{\mathrm{Q}}=36 / 25, what is the value of hQh_{\mathrm{Q}} ?
Medium•Mechanics
A particle of mass mm is moving in the xyx y-plane such that its velocity at a point (x,y)(x, y) is given as v→=α(yx^+2xy^)\overrightarrow{\mathrm{v}}=\alpha(y \hat{x}+2 x \hat{y}), where α\alpha is a non-zero constant. What is the force F⃗\vec{F} acting on the particle?
Medium•Mechanics
A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT=0.01\delta T=0.01 seconds and he measures the depth of the well to be L=20L=20 meters. Take the acceleration due to gravity g=10 ms−2g=10 \mathrm{~ms}^{-2} and the velocity of sound is 300 ms−1300 \mathrm{~ms}^{-1}. Then the fractional error in the measurement, δL/L\delta L / L, is closest to