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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?
A wind with speed $40 \text{ m/s}$ blows parallel to the roof of a house. The area of the roof is $250 \text{ m}^2$. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be: $(\rho_{air}=1.2 \text{ kg/m}^3)$
The pressure experienced by a swimmer $20 \text{ m}$ below the water surface in a lake is appropriately: (Given density of water = $10^3 \text{ kg m}^{-3}$, $g=10 \text{ m s}^{-2}$ and $1 \text{ atm} = 10^5 \text{ Pa}$)
Two particles of masses $m_1$ and $m_2$ move with initial velocities $u_1$ and $u_2$ respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy $E$. If the final velocities of particles are $v_1$ and $v_2$, then we must have:
The input resistance of a silicon transistor is $100\, \Omega$. Base current is changed by $40\, \mu\text{A}$ which results in a change in collector current by $2\text{ mA}$. This transistor is used as a common-emitter amplifier with a load resistance of $4\text{ k}\Omega$. The voltage gain of the amplifier is:
The displacement of a particle executing simple harmonic motion is given by $y = A_0 + A\sin\omega t + B\cos\omega t$. Then the amplitude of its oscillation is given by :
300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Taking g = 10 m/s², work done against friction is:
Copper of fixed volume $V$ is drawn into a wire of length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?
The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100\text{ cm}$ to stretch it by $1\text{ mm}$ is: (given: Young's modulus of the wire $Y = 2.0 \times 10^{11}\text{ N/m}^2$)
A steel wire can withstand a load up to $2940 \text{ N}$. A load of $150 \text{ kg}$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is (2008 E)
A student measured the diameter of a small steel ball using a screw gauge of least count $0.001$ cm. The main scale reading is $5$ mm and zero of circular scale division coincides with $25$ divisions above the reference level. If screw gauge has a zero error of $-0.004$ cm, the correct diameter of the ball is
An alkene "A" on reaction with $O_3$ and $Zn-H_2O$ gives propanone and ethanal in equimolar ratio. Addition of $HCl$ to alkene "A" gives "B" as the major product. The structure of product "B" is:
The Young's modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of:
A mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
A particle is moving such that its position coordinates $(x, y)$ are $(2\text{ m}, 3\text{ m})$ at time $t = 0$, $(6\text{ m}, 7\text{ m})$ at time $t = 2\text{ s}$ and $(13\text{ m}, 14\text{ m})$ at time $t = 5\text{ s}$. Average velocity vector ($\mathbf{v}_{av}$) from $t = 0$ to $t = 5\text{ s}$ is:
A particle of mass $10 \text{ g}$ moves along a circle of radius $6.4 \text{ cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to $8 \times 10^{-4} \text{ J}$ by the end of the second revolution after the beginning of the motion?
A particle has an initial velocity $(2\hat{i} + 3\hat{j})$ and an acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10 \text{ s}$ will be:
A projectile is fired from the surface of the earth with a velocity of $5 \text{ m/s}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \text{ m/s}$ at the same angle follows a trajectory, which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in $\text{m/s}^2$) is: [Given, $g = 9.8 \text{ m/s}^2$]
A block of mass $10 \text{ kg}$, moving in the $x$-direction with a constant speed of $10 \text{ m/s}$, is subjected to a retarding force $F = 0.1x \text{ J/m}$ during its travel from $x = 20 \text{ m}$ to $30 \text{ m}$. Its final kinetic energy will be:
Select the correct events that occur during inspiration. (a) Contraction of diaphragm (b) Contraction of external inter-costal muscles (c) Pulmonary volume decreases (d) Intra pulmonary pressure increases