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Physics · WORK, ENERGY AND POWER
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Physics · WORK, ENERGY AND POWER
A woman pushes a crate on a rough floor. For the first \( 12\text{ m} \), she applies a constant force of \( 120\text{ N} \). Over the next \( 8\text{ m} \), her applied force decreases linearly to \( 40\text{ N} \). Throughout the motion, an opposing frictional force of \( 60\text{ N} \) acts on the crate. The net work done on the crate during the entire \( 20\text{ m} \) displacement is:
Read answer →Physics · WORK, ENERGY AND POWER
A bob of mass \( m \) is attached to a light string of length \( L \) and oscillates in a vertical circle. If the horizontal velocity imparted at the lowest point \( A \) is just sufficient for the string to become slack at the topmost point \( C \), the ratio of the tension in the string at the lowest point \( A \) to that at the horizontal position \( B \) is:
Read answer →Physics · WORK, ENERGY AND POWER
An electric pump is used to fill a water tank of capacity \( 30\text{ m}^3 \) located at a height of \( 40\text{ m} \) above the ground in \( 15\text{ minutes} \). If the overall efficiency of the pump is \( 30\% \) and \( g = 9.8\text{ m s}^{-2} \), the electrical power consumed by the pump is:
Read answer →Physics · WORK, ENERGY AND POWER
A running athlete of mass \( 70\text{ kg} \) runs with a speed of \( 10\text{ m s}^{-1} \) having kinetic energy \( K_1 \). A stone of mass \( 1\text{ kg} \) dropped from a height of \( 10\text{ m} \) reaches the ground with kinetic energy \( K_2 \approx 10^2\text{ J} \). The ratio \( \frac{K_1}{K_2} \) is equal to:
Read answer →Physics · WORK, ENERGY AND POWER
A spherical raindrop of radius \( 2\text{ mm} \) falls from a height of \( 500\text{ m} \) above the ground. It experiences air resistance such that its speed upon reaching the ground is \( 10\text{ m s}^{-1} \). Taking \( g = 10\text{ m s}^{-2} \) and the density of water as \( 10^3\text{ kg m}^{-3} \), the work done by the resistive force during the entire descent is:
Read answer →Physics · WORK, ENERGY AND POWER
A raindrop of mass \( 1.00\text{ g} \) falls from a height of \( 1.00\text{ km} \) from rest and hits the ground with a speed of \( 50.0\text{ m s}^{-1} \). Taking \( g = 10\text{ m s}^{-2} \), the work done by the unknown resistive force of the air is:
Read answer →Physics · WORK, ENERGY AND POWER
A particle moves along the x-axis under the influence of a conservative force whose potential energy is given by \( V(x) = \alpha x^2 - \beta x \), where \( \alpha \) and \( \beta \) are positive constants. The force \( F(x) \) acting on the particle is:
Read answer →Physics · WORK, ENERGY AND POWER
Refer to the figure showing a bob of mass \( m \) suspended by a light string of length \( L \) undergoing circular motion in a vertical plane. When the bob reaches point \( B \) at the horizontal level, the magnitude of its total acceleration is:
Read answer →Physics · WORK, ENERGY AND POWER
A raindrop falling from a great height attains terminal speed when the opposing drag force balances gravity. If a falling raindrop of mass \( 3.5\times 10^{-5}\text{ kg} \) has attained a terminal speed of \( 9.0\text{ m s}^{-1} \), its kinetic energy is closest to:
Read answer →Physics · WORK, ENERGY AND POWER
Given below are two statements: Statement I: The scalar product of two vectors is non-commutative, such that \( \mathbf{A}\cdot\mathbf{B} = -\mathbf{B}\cdot\mathbf{A} \). Statement II: The scalar product of two vectors does not obey the distributive law over vector addition. In the light of the above statements, choose the most appropriate answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
A body of mass \( 0.5\text{ kg} \) travels along the x-axis with a velocity given by \( v(x) = a x^{3/2} \), where \( a = 5\text{ m}^{-1/2}\text{ s}^{-1} \). The work done by the net force acting on the body during its displacement from \( x = 0 \) to \( x = 2\text{ m} \) is:
Read answer →Physics · WORK, ENERGY AND POWER
Referring to the force-displacement graph shown below, an applied force F acts on a block moving along a straight line on a rough horizontal surface against a constant friction force \( f = -50 N \). The total net work done on the block over the entire \( 20 m \) distance is:
Read answer →Physics · WORK, ENERGY AND POWER
Given below are two statements: Statement I: When the angle \( \theta \) between the force vector and the displacement vector is obtuse (\( 90^\circ < \theta \le 180^\circ \)), the work done by the force is negative. Statement II: Kinetic energy of a particle of mass \( m \) moving with velocity \( \mathbf{v} \) is a vector quantity directed along the direction of motion. In the light of the above statements, choose the most appropriate answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
A variable force \( F(x) = -cx^3 \) (where \( c = 2\text{ N m}^{-3} \)) acts on a particle of mass \( 0.25\text{ kg} \) moving along the \( x \)-axis. If the particle is released from rest at \( x = 2\text{ m} \), its speed when it passes through the origin \( x = 0 \) is:
Read answer →Physics · WORK, ENERGY AND POWER
Consider the following statements regarding the concept of potential energy: (A) Potential energy is the 'stored energy' possessed by an object by virtue of its position or configuration. (B) Stretched bow-strings and compressed springs possess potential energy. (C) Readjustment of dislocations along fault lines in the Earth's crust releases stored potential energy, causing earthquakes. (D) For an object at height \( h \) with potential energy \( V(h) = mgh \), the gravitational force is given by \( F = +\frac{dV}{dh} \). Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
A block of mass \( m_1 = 2\text{ kg} \) moving with a speed of \( 6\text{ m s}^{-1} \) collides with a stationary block of mass \( m_2 = 4\text{ kg} \). If the collision is completely inelastic, what is the ratio of the kinetic energy lost during the collision to the initial kinetic energy of the system?
Read answer →Physics · WORK, ENERGY AND POWER
A bullet of mass \( 40.0\text{ g} \) travelling at \( 250\text{ m s}^{-1} \) penetrates a thick wooden target of thickness \( 5.0\text{ cm} \) and emerges with only \( 16\% \) of its initial kinetic energy. The average resistive force exerted by the target on the bullet is:
Read answer →Physics · WORK, ENERGY AND POWER
A test car of mass \( 1200\text{ kg} \) moving at a speed of \( 72\text{ km h}^{-1} \) on a smooth horizontal track collides with a horizontally mounted buffer spring of spring constant \( 4.8 \times 10^4\text{ N m}^{-1} \). The maximum compression of the spring is:
Read answer →Physics · WORK, ENERGY AND POWER
Match List-I with List-II: List-I (Physical Quantity / Concept) List-II (Dimension / Mathematical Expression) A Work done by spring force from \( 0 \) to \( x_m \) I \( [\text{M}\text{L}^2\text{T}^{-3}] \) B Spring constant \( k \) II \( -\frac{1}{2}kx_m^2 \) C Ratio \( k/m \) for oscillating block III \( [\text{T}^{-2}] \) D Instantaneous Power IV \( [\text{M}\text{T}^{-2}] \) Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
If the reference point for the zero of potential energy of a physical system is shifted by an arbitrary constant \( C_0 \), which of the following physical quantities will change?
Read answer →Physics · WORK, ENERGY AND POWER
Match List-I with List-II: List-I (Unit of Work/Energy) List-II (Equivalent Value in Joules) A 1 erg I \( 3.6 \times 10^6 \text{ J} \) B 1 electron volt (eV) II \( 4.186 \text{ J} \) C 1 calorie (cal) III \( 1.6 \times 10^{-19} \text{ J} \) D 1 kilowatt hour (kWh) IV \( 10^{-7} \text{ J} \) Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
A heavy body of mass \( M \) moving with speed \( u \) collides elastically with a very light body of mass \( m \) (\( m \ll M \)) initially at rest. The speed of the lighter body after the collision is:
Read answer →Physics · WORK, ENERGY AND POWER
