JEE MAIN - Physics (2024 - 1st February Morning Shift)
- 1Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in $\mathrm{ms}^{-2}$ is :
(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :
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Antwort(D)2 - 7A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in $\mathrm{rad} / \mathrm{s}$ is, :Antwort(C)40
- 11A parallel plate capacitor has a capacitance $\mathrm{C}=200~ \mathrm{pF}$. It is connected to $230 \mathrm{~V}$ ac supply with an angular frequency $300~ \mathrm{rad} / \mathrm{s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :Antwort(B)$13.8 ~\mu \mathrm{A}$ and $13.8 ~\mu \mathrm{A}$
- 13The radius $(\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as
$$ \begin{aligned} & \mathrm{r}=(0.35 \pm 0.05) ~\mathrm{cm} \\\\ & \mathrm{R}=(100 \pm 10) ~\mathrm{ohm} \\\\ & l=(15 \pm 0.2)~ \mathrm{cm} \end{aligned} $$
The percentage error in resistivity of the material of the wire is :Antwort(D)$39.9 \%$ - 14Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2 \mathrm{~V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :Antwort(A)$\frac{1}{4} \mathrm{CV}^2$
- 15A simple pendulum of length $1 \mathrm{~m}$ has a wooden bob of mass $1 \mathrm{~kg}$. It is struck by a bullet of mass $10^{-2} \mathrm{~kg}$ moving with a speed of $2 \times 10^2 \mathrm{~ms}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )Antwort(A)$0.20 \mathrm{~m}$
- 16The pressure and volume of an ideal gas are related as $\mathrm{PV}^{\frac{3}{2}}=\mathrm{K}$ (Constant). The work done when the gas is taken from state $A\left(P_1, V_1, T_1\right)$ to state $B\left(P_2, V_2, T_2\right)$ is :Antwort(D)$2\left(\mathrm{P}_1 \mathrm{~V}_1-\mathrm{P}_2 \mathrm{~V}_2\right)$
- 18A particle moving in a circle of radius $\mathrm{R}$ with uniform speed takes time $\mathrm{T}$ to complete one revolution.
If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :Antwort(A)$\sin ^{-1}\left[\frac{2 \mathrm{gT}^2}{\pi^2 \mathrm{R}}\right]^{\frac{1}{2}}$ - 21A rectangular loop of sides $12 \mathrm{~cm}$ and $5 \mathrm{~cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively, moves with a velocity of $5 \mathrm{~cm} / \mathrm{s}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of $10^{-3} \mathrm{~T} / \mathrm{cm}$ along the negative $x$ direction and it is decreasing with time at the rate of $10^{-3} \mathrm{~T} / \mathrm{s}$. If the resistance of the loop is $6 \mathrm{~m} \Omega$, the power dissipated by the loop as heat is __________ $\times 10^{-9} \mathrm{~W}$.Antwort216
- 22A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is ___________ kg.
(Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )Antwort9600 - 23Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be __________.
(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )Antwort3 - 24A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16 t$, where $x$ is in $\mathrm{m}$ and $\mathrm{t}$ is in $\mathrm{s}$.
The velocity of the particle when its acceleration becomes zero is _________ $\mathrm{m} / \mathrm{s}$.Antwort52 - 26A regular polygon of 6 sides is formed by bending a wire of length $4 \pi$ meter.
If an electric current of $4 \pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7} \mathrm{~T}$.
The value of $x$ is _________.Antwort72 - 28Three identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is ___________ .Antwort3
- 29A tuning fork resonates with a sonometer wire of length $1 \mathrm{~m}$ stretched with a tension of $6 \mathrm{~N}$. When the tension in the wire is changed to $54 \mathrm{~N}$, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ $\mathrm{Hz}$.Antwort6
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