A rod of length 5 L is bent right angle keeping one side length as 2 L . The position of the centre of mass of the system : (Consider $\mathrm{L}=10\mathrm{cm}$)

Consider two blocks A and B of masses $m_1=10\mathrm{kg}$ and ${\mathrm{m}}_2=5\mathrm{kg}$ that are placed on a frictionless table. The block A moves with a constant speed $v=3\mathrm{m}/\mathrm{s}$ towards the block B kept at rest. A spring with spring constant $\mathrm{k}=3000\mathrm{N}/\mathrm{m}$ is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

The fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = $2\times 10^9$ N m${}^{-2}$, density of water = $10^3$ kg m${}^{-3}$, acceleration due to gravity $g = 10$ m s${}^{-2}$.

A tube of length $L$ is shown in the figure. The radius of cross section at the point $(1)$ is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is $2\mathrm{m}/\mathrm{s}$, then velocity of water leaving the point (2) will be

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

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 kg m-3)

Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x_2$ under the tension of 7 N . For the elongation of $\left(5x_1-2x_2\right)$, the tension in the spring will be,

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density $1000\mathrm{kg}/{\mathrm{m}}^3$. If the pressure inside the bubble is $2100\mathrm{N}/{\mathrm{m}}^2$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use $g=10\mathrm{m}/{\mathrm{s}}^2$ )

The amount of work done to break a big water drop of radius ' $R$ ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be

In the experiment for measurement of viscosity ' $\eta$ ' of given liquid with a ball having radius $R$, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of $\eta$ will change. Choose the correct answer from the options given below:

Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

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 $P\times 10^{11}{\text{Nm}}^{-2}$, where the value of $P$ is: (Take $g=3\pi {\text{m/s}}^2$)

Two wires A and B are made of same material having ratio of lengths $\frac{L_A}{L_B}=\frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B}=2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with 30° inclined with the vertical. The length of water risen in the capillary is _______ cm. (Take $g=9.8{\text{ m/s}}^2$)

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area $0.5{\mathrm{m}}^2$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the crosssectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: $$\left(\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\right)$$

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^5\mathrm{N}$ at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $\theta$ of the rod axis from its original position would be : (shear moduli, $G=10^{10}\mathrm{N}/{\mathrm{m}}^2$ )

Two liquids $A$ and $B$ have ${\theta }_A$ and ${\theta }_B$ as contact angles in a capillary tube. If $K=\cos {\theta }_A/\cos {\theta }_B$, then identify the correct statement: