An object of mass $500\; \mathrm{g}$, intitally at rest acted upon by a variable force where $\mathrm{X}$ component varies with $\mathrm{X}$ in the manner shown. The velocities of the object at point $X=8 \;\mathrm{m}$ and $X=12\; \mathrm{m},$ would be the respective values
An object of mass $500\; \mathrm{g}$, intitally at rest acted upon by a variable force where $\mathrm{X}$ component varies with $\mathrm{X}$ in the manner shown. The velocities of the object at point $X=8 \;\mathrm{m}$ and $X=12\; \mathrm{m},$ would be the respective values
- [NEET 2019]
- A
$18 \;\mathrm{m} / \mathrm{s}$ and $24.4 \;\mathrm{m} / \mathrm{s}$
- B
$23 \;\mathrm{m} / \mathrm{s}$ and $24.4 \;\mathrm{m} / \mathrm{s}$
- C
$23 \;\mathrm{m} / \mathrm{s}$ and $20.6 \;\mathrm{m} / \mathrm{s}$
- D
$18 \;\mathrm{m} / \mathrm{s}$ and $20.6 \;\mathrm{m} / \mathrm{s}$
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- [AIPMT 2001]
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]
The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
$(a)$ work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
$(b)$ work done by gravitational force in the above case,
$(c)$ work done by friction on a body sliding down an inclined plane,
$(d)$ work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,
$(e)$ work done by the resistive force of air on a vibrating pendulum in bringing it to rest.
The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:
$(a)$ work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
$(b)$ work done by gravitational force in the above case,
$(c)$ work done by friction on a body sliding down an inclined plane,
$(d)$ work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,
$(e)$ work done by the resistive force of air on a vibrating pendulum in bringing it to rest.
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]