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Physics · WORK, ENERGY AND POWER
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Physics · WORK, ENERGY AND POWER
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The scalar product of two mutually perpendicular non-zero vectors is always zero. Reason (R): The scalar product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is defined as \( \mathbf{A}\cdot\mathbf{B} = AB\cos\theta \), and \( \cos 90^\circ = 0 \). In the light of the above statements, choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
Match List-I with List-II: List-I List-II A Work done I \( [\text{M}\text{T}^{-2}] \) B Spring constant II \( [\text{M}\text{L}^2\text{T}^{-3}] \) C Power III \( -\frac{dV}{dx} \) D Conservative force IV \( [\text{M}\text{L}^2\text{T}^{-2}] \) Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
A bob suspended by a string executes vertical circular motion. If the string becomes slack exactly at the highest point \( C \) and is simultaneously cut at that very instant, what is the subsequent trajectory of the bob?
Read answer →Physics · WORK, ENERGY AND POWER
A force \( \mathbf{F} = (4\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - 2\hat{\mathbf{k}})\text{ N} \) acts on a particle, displacing it from \( \mathbf{r}_1 = (2\hat{\mathbf{i}} - \hat{\mathbf{j}} + 3\hat{\mathbf{k}})\text{ m} \) to \( \mathbf{r}_2 = (5\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - \hat{\mathbf{k}})\text{ m} \). The work done by the force is:
Read answer →Physics · WORK, ENERGY AND POWER
Given below are two statements: Statement I: When non-conservative forces act on a body, the total mechanical energy \( E = K + V \) is always conserved. Statement II: The work done by non-conservative forces is equal to the change in the total mechanical energy of the system, \( \Delta E = W_{nc} \). 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 car of mass \( 1000\text{ kg} \) moving with a speed of \( 18.0\text{ km/h} \) on a smooth horizontal road collides with a horizontally mounted spring of spring constant \( 6.25 \times 10^3\text{ N m}^{-1} \). The maximum compression of the spring will be:
Read answer →Physics · WORK, ENERGY AND POWER
A bullet of mass \( 50.0\text{ g} \) fired with speed \( 200\text{ m s}^{-1} \) strikes a soft plywood board. It emerges from the board with only \( 10\% \) of its initial kinetic energy. The emergent speed of the bullet is closest to:
Read answer →Physics · WORK, ENERGY AND POWER
Consider the following statements regarding the work done by a variable force: (A) In one dimension, the total work done by a variable force \( F(x) \) from position \( x_i \) to \( x_f \) is equal to the area under the \( F(x) \) versus \( x \) curve between these limits. (B) The area under the force-displacement curve on the negative side of the force axis contributes positively to the work done. (C) The work-energy theorem is valid for variable forces as well as constant forces. (D) Work done has the dimensional formula \( [\text{M}\text{L}^2\text{T}^{-2}] \). Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
The potential energy of a particle of mass \( 1\text{ kg} \) moving along the \( x \)-axis is given by \( V(x) = (x^3 - 6x^2 + 9x + 5)\text{ J} \). If the total mechanical energy of the particle is \( 15\text{ J} \), its maximum speed is:
Read answer →Physics · WORK, ENERGY AND POWER
For a particle of mass \( m \) moving in one dimension under a variable net force \( F \), the time rate of change of kinetic energy \( \frac{dK}{dt} \) is mathematically expressed as:
Read answer →Physics · WORK, ENERGY AND POWER
Which of the following statements correctly highlights the fundamental limitation in information content when going from Newton's second law to the Work-Energy theorem?
Read answer →Physics · WORK, ENERGY AND POWER
Match List-I with List-II: List-I (Physical Situation) List-II (Work Done by the Specified Force) A Moon orbiting Earth in a circular orbit I Zero work because force and displacement are mutually perpendicular B Weightlifter holding a 150 kg barbell steadily overhead II Negative work opposing displacement C Kinetic friction acting on a skidding bicycle III Zero work because displacement is zero D Raindrop falling freely under downward gravity IV Positive work in direction of displacement Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
An electron has a kinetic energy of \( 10\text{ keV} \) and a proton has a kinetic energy of \( 100\text{ keV} \). Taking the mass of an electron as \( 9.11 \times 10^{-31}\text{ kg} \) and proton mass as \( 1.67 \times 10^{-27}\text{ kg} \), the ratio of the speed of the electron to that of the proton is approximately:
Read answer →Physics · WORK, ENERGY AND POWER
A raindrop of mass \( 1.50\text{ g} \) falls from a height of \( 1.20\text{ km} \) under the action of gravity and an opposing air resistance. If it hits the ground with a terminal speed of \( 40.0\text{ m s}^{-1} \) (taking \( g = 10\text{ m s}^{-2} \)), the work done by the resistive force is:
Read answer →Physics · WORK, ENERGY AND POWER
A force \( \mathbf{F} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}} - 5\hat{\mathbf{k}})\text{ N} \) acts on a particle and produces a displacement \( \mathbf{d} = (5\hat{\mathbf{i}} + 4\hat{\mathbf{j}} + 3\hat{\mathbf{k}})\text{ m} \). The cosine of the angle \( \theta \) between the force and displacement vectors is:
Read answer →Physics · WORK, ENERGY AND POWER
A block on a frictionless horizontal table is connected to a spring of spring constant \( k \). If the work done by the spring force when the block moves from \( x = x_i \) to \( x = x_f \) is zero, then which of the following conditions must hold true?
Read answer →Physics · WORK, ENERGY AND POWER
Consider the following statements regarding the work-energy theorem and mechanical principles: (A) The work done by a force depends on the choice of the reference frame. (B) For an isolated two-body system, the sum of internal mutual forces is always zero, so the sum of work done by mutual forces \( W_{12} + W_{21} \) must always be zero. (C) The work-energy theorem is valid in non-inertial reference frames provided pseudo forces are included. (D) In an elastic collision, total kinetic energy is conserved at each and every instant during the impact. Choose the correct answer from the options given below:
Read answer →Physics · WORK, ENERGY AND POWER
A fast neutron collides elastically and head-on with a stationary nucleus of mass number \( A \). The fraction of its initial kinetic energy retained by the neutron after the collision is:
Read answer →Physics · WORK, ENERGY AND POWER
An electric heater rated at \( 1500\text{ W} \) is operated continuously for 8 hours daily for 30 days. The electrical energy consumed in this period expressed in Joules is:
Read answer →Physics · WORK, ENERGY AND POWER
A block of mass \( m \) is released from rest at the top of a smooth inclined plane of height \( h \). If the angle of inclination of the plane is doubled while keeping the vertical height \( h \) fixed, the speed of the block at the bottom of the plane will:
Read answer →Physics · WORK, ENERGY AND POWER
The bob of a simple pendulum of length \( L = 1.5\text{ m} \) is released from rest from a horizontal position. During its downward swing to the lowermost point, \( 5\% \) of its initial mechanical energy is dissipated against air resistance. Taking \( g = 10\text{ m s}^{-2} \), the speed of the bob at the lowest point is:
Read answer →Physics · WORK, ENERGY AND POWER
A body of mass \( m_1 \) moving with initial velocity \( v_{1i} \) collides head-on completely inelastically with a stationary body of mass \( m_2 \). The fraction of initial kinetic energy lost in the collision is:
Read answer →Physics · WORK, ENERGY AND POWER
