JEE Main Physics — Mechanics previous year questions with solutions.
A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of $25 \pi \mathrm{Nm}$ for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ________ m.
The torque due to the force $(2 \hat{i}+\hat{j}+2 \hat{k})$ about the origin, acting on a particle whose position vector is $(\hat{i}+\hat{j}+\hat{k})$, would be
A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______ $\times 10^{10} \mathrm{~J}$. (Mass of earth $=6 \times 10^{24} \mathrm{~kg}$, Radius of earth $=$ $6.4 \times 10^6 \mathrm{~m}$, Gravitational constant $=$ $\left.6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}\right)$
Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below
The maximum percentage error in the measurment of density of a wire is [Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$ radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$ length of wire $=(10.00 \pm 0.05) \mathrm{cm}]$
A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water ? (Given : density of water $=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant. Reason (R) : For a central force field the angular momentum is a constant. In the light of the above statements, choose the most appropriate answer from the options given below :
A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be : 
A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$. The value of $x$ is ______ , where $M$ and $R$ are the mass and radius of earth, respectively. ( G is the gravitational constant)
For an experimental expression $y=\frac{32.3 \times 1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write
Given below are two statements: one is labelled as Assertion $\mathrm{A}$ and the other is labelled as Reason $\mathrm{R}$ Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth. Reason $\mathrm{R}$ : The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the option given below
A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius $\mathrm{R} / 2$ is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above. 
Match List-I with List-II. $\begin{array}{ll} \text{List-I} & \text{List-II} \\ \text{(A) Heat capacity of body} & \text{(I) } \mathrm{J} \mathrm{kg}^{-1} \\ \text{(B) Specific heat capacity of body} & \text{(II) } \mathrm{JK}^{-1} \\ \text{(C) Latent heat} & \text{(III) } \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} \\ \text{(D) Thermal conductivity} & \text{(IV) } \mathrm{Jm}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1} \end{array}$ Choose the correct answer from the options given below :
A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is
Match List - I with List - II.  Choose the correct answer from the options given below :
As shown below, bob \(A\) of a pendulum having massless string of length ' \(R\) ' is released from \(60^{\circ}\) to the vertical. It hits another bob \(B\) of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.) 
The maximum percentage error in the measurment of density of a wire is [Given, mass of wire $=(0.60 \pm 0.003) \mathrm{g}$ radius of wire $=(0.50 \pm 0.01) \mathrm{cm}$ length of wire $=(10.00 \pm 0.05) \mathrm{cm}]$
Two particles are located at equal distance from origin. The position vectors of those are represented by $\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}$ and $\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}$, respectively. If both the vectors are at right angle to each other, the value of $\mathrm{n}^{-1}$ is _____ .
A person measures mass of 3 different particles as $435.42 \mathrm{~g}, 226.3 \mathrm{~g}$ and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.
A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $\mathrm{P} \times 10^{11} \mathrm{Nm}^{-2}$, where the value of P is: (Take $\left.\mathrm{g}=3 \pi \mathrm{~m} / \mathrm{s}^2\right)$
The increase in pressure required to decrease the volume of a water sample by $0.2 \%$ is $\mathrm{P} \times 10^5 \mathrm{Nm}^{-2}$. Bulk modulus of water is $2.15 \times 10^9 \mathrm{Nm}^{-2}$. The value of P is $\ldots\ldots$
Two slabs with square cross section of different materials $(1,2)$ with equal sides $(l)$ and thickness $\mathrm{d}_1$ and $\mathrm{d}_2$ such that $\mathrm{d}_2=2 \mathrm{~d}_1$ and $l \gt \mathrm{d}_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_2=2 \theta_1$. If the shear moduli of material 1 is $4 \times 10^9 \mathrm{~N} / \mathrm{m}^2$, then shear moduli of material 2 is $\mathrm{x} \times 10^9 \mathrm{~N} / \mathrm{m}^2$, where value of $x$ is ________.
The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).
A uniform solid cylinder of mass ' $m$ ' and radius ' $r$ ' rolls along an inclined rough plane of inclination $45^{\circ}$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be