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The amount of energy required to form a soap bubble of radius $2 \text{ cm}$ from a soap solution is nearly: (Given: surface tension of soap solution $= 0.03 \text{ N m}^{-1}$)
A body of mass $6 \text{ kg}$ is moving from its initial position $A$ to the next position $B$ as shown in the figure. From $A$ to $B$, the value of the momentum of the body is (in SI units):
A certain number of spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R$ and volume $V$. If $T$ is the surface tension of the liquid, then:
The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from $T_1$ K to $T_2$ K is:
A bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be:
Wavelength of ray of light is 0.00006 m. It is equal to:
An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by $60^\circ$ is $W$. Now the torque required to keep the magnet in this new position is:
A particle of mass $m$ is projected with velocity $v$ making an angle of $45^\circ$ with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:
Given below are two statements: Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R): A coil spring of copper has more tensile strength than a steel spring of the same dimensions.
A soap bubble, having a radius of $1 \text{ mm}$, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2} \text{ N/m}$. The pressure inside the bubble equals the pressure at a point $Z_0$ below the free surface of the water in a container. Taking $g = 10 \text{ m/s}^2$ and the density of water $\rho = 10^3 \text{ kg/m}^3$, the value of $Z_0$ is:
The length of a magnetized iron bar is $L$ and its magnetic moment is $M$. When this bar is bent to form a semicircle its magnetic moment is:
The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $P$, the fractional decrease in radius will be:
A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It:
A convex lens and a concave lens, each having the same focal length of $25\text{ cm}$, are put in contact to form a combination of lenses. The power in dioptres of the combination is:
Select the correct option based on the statements: Statement I: The magnetic field of a circular loop at very far away point on the axial line varies with distance as like that of a magnetic dipole. Statement II: The magnetic field due to magnetic dipole varies inversely with the square of the distance from the centre on the axial line.
A soap bubble, having radius of $1\text{ mm}$, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2}\text{ N/m}$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g = 10\text{ m/s}^2$, density of water $= 10^3\text{ kg/m}^3$, the value of $Z_0$ is :
Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is:
Match List-I with List-II. **List-I (Material)** (A) Diamagnetic (B) Ferromagnetic (C) Paramagnetic (D) Non-magnetic **List-II (Susceptibility $\chi$)** (I) $\chi = 0$ (II) $0 > \chi \ge -1$ (III) $\chi \gg 1$ (IV) $0 < \chi < \epsilon$ (a small positive number) Choose the correct answer from the options given below:
A wire of length $L$, area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is: