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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?
When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of 60$^{\circ}$ with horizontal, it can travel a distance $x_1$ along the plane. But when the inclination is decreased to 30$^{\circ}$ and the same object is shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be:
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 $Y = 2.0 \times 10^{11}\text{ N/m}^2$)
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
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)
Two particles of masses $m_1, m_2$ move with initial velocities $u_1$ and $u_2$. On collision, one of the particles gets excited to a higher level, after absorbing energy $\varepsilon$. If the final velocities of the particles are $v_1$ and $v_2$, then we must have:
The maximum elongation of a steel wire of $1 \text{ m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^8 \text{ N m}^{-2}$ and $2 \times 10^{11} \text{ N m}^{-2}$, is:
Which of the following is not the product of dehydration of the given alcohol?