State the importance of work energy theorem. Whether the work energy theorem is a scalar or a vector ?
State the importance of work energy theorem. Whether the work energy theorem is a scalar or a vector ?
$(1)$ If the change in kinetic energy $\Delta K$ of a body is zero, then the work done on the body is zero and its kinetic energy remains constant and hence the speed of the body remains constant.
For example : the speed of a particle in uniform circular motion is constant and work done is zero.
$(2)$ If the displacement of a body is in the same direction of force or displacement is in direction of component of force then the work done on the body and hence the kinetic energy of body increases.
For example, free fall body.
$(3)$ If the displacement of a body is opposite in the direction of force or displacement is in the opposite direction of component of force then the work done by the body and hence, the kinetic energy of body decreases.
Similar Questions
Given below are two statements:
Statement $I:$ A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement $II:$ A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of given statements, choose the most appropriate answer from the options given below.
Given below are two statements:
Statement $I:$ A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement $II:$ A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of given statements, choose the most appropriate answer from the options given below.
- [JEE MAIN 2023]
Column $II$ shows five systems in which two objects are labelled as $\mathrm{X}$ and $\mathrm{Y}$. Also in each case a point $\mathrm{P}$ is shown. Column $I$ gives some statements about $\mathrm{X}$ and/or $\mathrm{Y}$. Match these statements to the appropriate system$(s)$ from Column $II$.
Column $I$
Column $II$
$(A)$ The force exerted by $\mathrm{X}$ on $\mathrm{Y}$ has a magnitude $\mathrm{Mg}$.
$Image$ Block $Y$ of mass $M$ left on a fixed inclined plane $\mathrm{X}$, slides on it with a constant velocity.
$(B)$ The gravitational potential energy of $\mathrm{X}$ is continuously increasing.
$Image$ Two ring magnets $\mathrm{Y}$ and $\mathrm{Z}$, each of mass $M$, are kept in frictionless vertical plastic stand so that they repel each other. $Y$ rests on the base $X$ and $\mathrm{Z}$ hangs in air in equilibrium. $\mathrm{P}$ is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity.
$(C)$ Mechanical energy of the system $\mathrm{X}+\mathrm{Y}$ is continuously decreasing.
$Image$ A pulley $Y$ of mass $m_0$ is fixed to a table through a clamp $X$. A block of mass $M$ hangs from a string that goes over the pulley and is fixed at point $\mathrm{P}$ of the table. The whole system is kept in a lift that is going down with a constant velocity.
$(D)$ The torque of the weight of $\mathrm{Y}$ about point $\mathrm{P}$ is zero.
$Image$ A sphere $\mathrm{Y}$ of mass $M$ is put in a nonviscous liquid $\mathrm{X}$ kept in a container at rest. The sphere is released and it moves down in the liquid.
$Image$ A sphere $\mathrm{Y}$ of mass $M$ is falling with its terminal velocity in a viscous liquid $\mathrm{X}$ kept in a container.
Column $II$ shows five systems in which two objects are labelled as $\mathrm{X}$ and $\mathrm{Y}$. Also in each case a point $\mathrm{P}$ is shown. Column $I$ gives some statements about $\mathrm{X}$ and/or $\mathrm{Y}$. Match these statements to the appropriate system$(s)$ from Column $II$.
| Column $I$ | Column $II$ |
| $(A)$ The force exerted by $\mathrm{X}$ on $\mathrm{Y}$ has a magnitude $\mathrm{Mg}$. | $Image$ Block $Y$ of mass $M$ left on a fixed inclined plane $\mathrm{X}$, slides on it with a constant velocity. |
| $(B)$ The gravitational potential energy of $\mathrm{X}$ is continuously increasing. | $Image$ Two ring magnets $\mathrm{Y}$ and $\mathrm{Z}$, each of mass $M$, are kept in frictionless vertical plastic stand so that they repel each other. $Y$ rests on the base $X$ and $\mathrm{Z}$ hangs in air in equilibrium. $\mathrm{P}$ is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity. |
| $(C)$ Mechanical energy of the system $\mathrm{X}+\mathrm{Y}$ is continuously decreasing. | $Image$ A pulley $Y$ of mass $m_0$ is fixed to a table through a clamp $X$. A block of mass $M$ hangs from a string that goes over the pulley and is fixed at point $\mathrm{P}$ of the table. The whole system is kept in a lift that is going down with a constant velocity. |
| $(D)$ The torque of the weight of $\mathrm{Y}$ about point $\mathrm{P}$ is zero. | $Image$ A sphere $\mathrm{Y}$ of mass $M$ is put in a nonviscous liquid $\mathrm{X}$ kept in a container at rest. The sphere is released and it moves down in the liquid. |
| $Image$ A sphere $\mathrm{Y}$ of mass $M$ is falling with its terminal velocity in a viscous liquid $\mathrm{X}$ kept in a container. |
- [IIT 2009]
A rough inclined plane is placed on car moving with a constant velocity $u$ on horizontal ground. A block of mass $ M$ rests on the inclined plane. Is any work done by force of friction between the block and inclined plane ? Is there then a dissipation of energy ?
A rough inclined plane is placed on car moving with a constant velocity $u$ on horizontal ground. A block of mass $ M$ rests on the inclined plane. Is any work done by force of friction between the block and inclined plane ? Is there then a dissipation of energy ?
A ball of mass $m$ moves with speed $v$ and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is
A ball of mass $m$ moves with speed $v$ and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is
A spherical ball of mass $20\, kg$ is stationary at the top of a hill of height $100 \,m$. It slides down a smooth surface to the ground, then climbs up another hill of height $30 \,m$ and finally slides down to a horizontal base at a height of $20 \,m$ above the ground. The velocity attained by the ball is ............... $\mathrm{m} / \mathrm{s}$
A spherical ball of mass $20\, kg$ is stationary at the top of a hill of height $100 \,m$. It slides down a smooth surface to the ground, then climbs up another hill of height $30 \,m$ and finally slides down to a horizontal base at a height of $20 \,m$ above the ground. The velocity attained by the ball is ............... $\mathrm{m} / \mathrm{s}$
- [AIEEE 2005]