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Physics · WORK, ENERGY AND POWER
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Physics · WORK, ENERGY AND POWER
An ideal massless spring with spring constant \( k \) is compressed by an amount \( x_0 \) from its equilibrium position. The work that must be done by an external agent to further compress it by an additional amount \( 2x_0 \) is:
Read answer →Physics · WORK, ENERGY AND POWER
A trolley of mass \( 300\text{ kg} \) carrying a sandbag of mass \( 25\text{ kg} \) moves uniformly at a speed of \( 27\text{ km h}^{-1} \) on a frictionless track. Sand leaks out vertically through a hole in the bottom of the trolley at a constant rate of \( 0.05\text{ kg s}^{-1} \). What is the speed of the trolley after the sandbag is completely empty?
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In a one-dimensional elastic collision, a particle of mass \( m_1 \) moving with velocity \( v_{1i} \) hits a stationary particle of mass \( m_2 \). The fraction of initial kinetic energy transferred to the second particle is:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The absolute value of potential energy of a physical system at a given point has no unique physical significance; only differences in potential energy are physically meaningful. Reason (R): The point chosen as the zero reference level of potential energy is arbitrary. In the light of the above statements, choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
Given below are two statements: Statement I: The work-energy theorem provides complete dynamical vector information regarding the three-dimensional motion of a body, identical to Newton's second law. Statement II: The work-energy theorem is an integral form of Newton's second law obtained by integrating force over displacement, in which explicit temporal and directional information is integrated over. In the light of the above statements, choose the most appropriate answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
Consider the following statements regarding collisions and energy: (A) In every collision, the total linear momentum of an isolated system is strictly conserved at each instant. (B) In an inelastic collision, total mechanical energy is conserved during the deformation phase. (C) In a completely inelastic collision between two bodies, the maximum possible kinetic energy is lost. (D) Power delivered by a force is a scalar quantity with dimensions \( [\text{M}\text{L}^2\text{T}^{-3}] \). How many of the above statements are correct?
Read answer →Physics · WORK, ENERGY AND POWER
A woman pushes a trunk on a rough railway platform. She applies a force of \( 100\text{ N} \) over a distance of \( 10\text{ m} \). Thereafter, her applied force decreases linearly with distance to \( 50\text{ N} \) at \( 20\text{ m} \). If a constant opposing frictional force of \( 50\text{ N} \) acts on the trunk throughout, the net work done on the trunk over the entire \( 20\text{ m} \) distance is:
Read answer →Physics · WORK, ENERGY AND POWER
A block of mass \( m \) moving with speed \( v \) compresses a horizontal spring of spring constant \( k \) on a rough floor having coefficient of friction \( \mu \). The maximum compression \( x_m \) satisfies which of the following quadratic equations?
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Consider the following statements regarding conservative and non-conservative forces: (A) Work done by a conservative force along a closed path is zero. (B) Work done against friction on a body moving on a rough surface always results in a decrease of its mechanical energy. (C) In an inelastic collision, the total linear momentum is conserved, but total energy of the isolated system is not conserved. (D) A conservative force can be written as the negative gradient of potential energy, \( F(x) = -\frac{dV}{dx} \). How many of the above statements are correct?
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In a one-dimensional elastic collision, a fast-moving lighter particle of mass \( m_1 \) collides with a massive stationary target of mass \( m_2 \) (\( m_2 \gg m_1 \)). Immediately after the collision, the lighter mass:
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A ball of mass \( m_1 \) collides elastically and head-on with a stationary ball of mass \( m_2 \). If the first ball recoils with one-third of its initial speed, the ratio \( m_1 : m_2 \) is:
Read answer →Physics · WORK, ENERGY AND POWER
An elevator can carry a maximum load of \( 1800\text{ kg} \) (elevator + passengers) and moves upwards with a constant speed of \( 2\text{ m s}^{-1} \). A constant frictional force of \( 4000\text{ N} \) opposes its motion. Taking \( g = 10\text{ m s}^{-2} \), the minimum power delivered by the motor to the elevator is:
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A block of mass \( m \) moving with speed \( v \) collides with an uncompressed spring of stiffness \( k \) on a rough horizontal floor with coefficient of kinetic friction \( \mu \). If the maximum compression of the spring is \( x_m \), which equation correctly relates \( x_m \) to the system parameters?
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A particle of mass \( m \) moves under the action of a constant power source delivering power \( P \). Starting from rest at \( t = 0 \), the distance covered by the particle as a function of time \( t \) is proportional to:
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In the vector representation shown in the figure, vector \( \mathbf{B} \) is inclined at an angle \( \theta \) to vector \( \mathbf{A} \). Which expression correctly gives the scalar product \( \mathbf{A} \cdot \mathbf{B} \) in terms of the components and projections illustrated?
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Kilowatt-hour (\( \text{kWh} \)) is a practical unit of electrical power consumed in household circuits. Reason (R): Power is defined as the rate at which work is done or energy is transferred per unit time. In the light of the above statements, choose the correct answer from the options given below:
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Given below are two statements regarding a block oscillating on an ideal spring of constant \( k \): Statement I: The dimensional formula of the ratio \( k/m \) is \( [\text{T}^{-2}] \). Statement II: The speed of the block is maximum when it is at the equilibrium position (\( x = 0 \)). In the light of the above statements, choose the most appropriate answer from the options given below:
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A billiard ball moving with speed \( v \) undergoes an elastic collision with an identical stationary billiard ball. After collision, the first ball moves at an angle of \( 30^\circ \) to its initial line of motion. The speed of the second ball after the collision is:
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A bob of mass \( m \) is suspended by a light string of length \( L \). What minimum horizontal velocity \( v_0 \) must be imparted to the bob at its lowest point so that it completes a full vertical circular loop?
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In an elastic head-on collision between two bodies of masses \( m_1 \) and \( m_2 \) (\( m_2 \) initially at rest), the ratio of the final speed of \( m_1 \) to the final speed of \( m_2 \) is \( 1 : 4 \). If \( m_1 \) continues in its original direction of motion, then the ratio \( m_1 / m_2 \) is:
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A electrical appliance of rating \( 100\text{ W} \) operates continuously for \( 10\text{ hours} \). The electrical energy consumed by the appliance expressed in joules is:
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A body of mass \( m_1 \) moving with speed \( v_1 \) collides completely inelastically with a stationary body of mass \( m_2 \). The fractional loss of kinetic energy of the system \( \frac{\Delta K}{K_i} \) is given by:
Read answer →Physics · WORK, ENERGY AND POWER
