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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 $v$, then the speed of ejection of the liquid through the holes will be:
The potential energy between two atoms in a molecule is given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$, where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The atoms are in stable equilibrium when:
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: $(\rho_{air}=1.2 \text{ kg/m}^3)$
Water rises to a height $h$ in a capillary tube. If the length of the capillary tube above the surface of water is made less than $h$, then:
A body of mass $1\text{ kg}$ begins to move under the action of a time-dependent force $\vec{F}=(2t\hat i+3t^2\hat j)\text{ N}$, where $\hat i$ and $\hat j$ are unit vectors along the $x$ and $y$-axis. What power will be developed by the force at the time $t$?
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 $1 \text{ atm} = 10^5 \text{ Pa}$)
The heart of a man pumps $5 \text{ L}$ of blood through the arteries per minute at a pressure of $150 \text{ mm}$ of mercury. If the density of mercury is $13.6 \times 10^3 \text{ kg/m}^3$ and $g = 10 \text{ m/s}^2$, then the power of heart in watt is:
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:
A body of mass $1\text{ kg}$ is thrown upwards with a velocity $20\text{ ms}^{-1}$. It momentarily comes to rest after attaining a height of $18\text{ m}$. How much energy is lost due to air friction? ($g=10\text{ ms}^{-2}$)
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:
Which of the following statements is not true?
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 :
A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $v$, the power delivered to the particle is:
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:
When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire becomes $(L+l)$. The elastic potential energy stored in the extended wire 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 two nearest harmonics of a tube closed at one end and open at the other end are $220 \text{ Hz}$ and $260 \text{ Hz}$. What is the fundamental frequency of the system?
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 body initially at rest and sliding along a frictionless track from a height $h$ just completes a vertical circle of diameter $AB = D$. The height $h$ is equal to: