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A uniform force of $(3\hat{i} + \hat{j})$ N acts on a particle of mass 2 kg. The particle is displaced from the position $(2\hat{i} + \hat{k})$ m to the position $(4\hat{i} + 3\hat{j} - \hat{k})$ m. The work done by the force on the particle is:
The relation amongst the three elements of Earth's magnetic field, namely horizontal component $H$, vertical component $V$ and dip angle $\delta$ is: ($B_E$ = total magnetic field):
A particle is displaced through $(3\hat i+4\hat j)\text{ m}$ by force $2\hat i\text{ N}$. The work done is:
Given below are two statements: Assertion (A): Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. Reason (R): The magnetic monopoles do not exist. North and South poles occur in pairs, allowing vanishing net magnetic flux through the surface.
Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths $r_H : r_\alpha$ will be :
In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are 15 cm and 20 cm respectively. The density of the oil is: [take ρ_water = 1000 kg/m^3]
A body of mass $M$ at rest explodes into three pieces, two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3 \text{ m/s}$ and $4 \text{ m/s}$ respectively. The third piece will be thrown off with a velocity of:
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is:
Match List-I with List-II. **List-I (Material)** (A) Diamagnet (B) Paramagnet (C) Soft ferromagnet (D) Hard ferromagnet **List-II (Example)** (I) Alnico (II) Copper (III) Aluminium (IV) Gadolinium Choose the correct answer from the options given below:
An iron bar of length $L$ has a magnetic moment $M$. It is bent at the middle of its length such that the two arms make an angle $60^{\circ}$ with each other. The magnetic moment of this new magnet is:
A block of mass $50 \text{ kg}$ slides over a horizontal distance of $1 \text{ m}$. If the coefficient of friction between their surfaces is $0.2$, then work done against friction is:
Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is
A uniform force of $(3\hat{i} + \hat{j}) \text{ N}$ acts on a particle of mass $2 \text{ kg}$. Hence the particle is displaced from position $(2\hat{i} + \hat{k}) \text{ m}$ to position $(4\hat{i} + 3\hat{j} - \hat{k}) \text{ m}$. The work done by the force on the particle is:
The minimum work done in pulling up a block of wood weighing $2 \text{ kN}$ for a length of $10 \text{ m}$ on a smooth plane inclined at an angle of $15^\circ$ with the horizontal is (given $\sin 15^\circ = 0.2588$):
The cylindrical tube of a spray pump has radius $R$, one end of which has $n$ fine holes, each of radius $r$. If the speed of the liquid in the tube is $v$, the speed of the ejection of the liquid through the holes is:
A U-tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10 \text{ mm}$ above the water level on the other side. Meanwhile, the water rises by $65 \text{ mm}$ from its original level (see diagram). The density of the oil is:
Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$), having the same value of surface tension $T$, rise to the same height in three identical capillaries. The angles of contact $\theta_1, \theta_2$ and $\theta_3$ obey:
A force acts on a $30 \text{ gm}$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \text{ seconds}$ is:
An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, $1\text{ kg}$ first part moving with a velocity of $12\text{ m s}^{-1}$ and $2\text{ kg}$ second part moving with a velocity of $8\text{ m s}^{-1}$. If the third part flies off with a velocity of $4\text{ m s}^{-1}$, its mass would be:
The approximate depth of an ocean is $2700\text{ m}$. The compressibility of water is $45.4 \times 10^{-11}\text{ Pa}^{-1}$ and density of water is $10^3\text{ kg/m}^3$. What fractional compression of water will be obtained at the bottom of the ocean?