(D) Initial kinetic energy $(K_i)$ of the body is given by:$K_i = \frac{1}{2} m v^2 = \frac{1}{2} \times 25 \times (2)^2 = 50\, J$The work done agains

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(D) Initial kinetic energy $(K_i)$ of the body is given by:$K_i = \frac{1}{2} m v^2 = \frac{1}{2} \times 25 \times (2)^2 = 50\, J$The work done against the resistive force is equal to the area under the $F-x$ graph.Area = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4\, m \times 20\, N = 40\, J$According to the work-energy theorem,the final kinetic energy $(K_f)$ is:$K_f = K_i - W_{\text{resistive}}$$K_f = 50\, J - 40\, J = 10\, J$

Class 11 Physics Work, Energy, Power and Collision Work Done by Variable Force and Force-Displacement Graph

Medium

The graph between the resistive force $F$ acting on a body and the distance $x$ covered by the body is shown in the figure. The mass of the body is $25\, kg$ and the initial velocity is $2\, m/s$. When the distance covered by the body is $4\, m$,its kinetic energy would be .............. $J$.

A
$50$
B
$40$
C
$20$
D
$10$

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Class 11

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Work, Energy, Power and Collision

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Work Done by Variable Force and Force-Displacement Graph

The figure shows the relationship between force and position. What is the work done by the force for the displacement of the object from $x = 1 \; cm$ to $x = 5 \; cm$ in ergs?

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What will be the area under the graph of variable force versus position?

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The components of a force acting on a particle vary according to the graphs shown. To reach point $B\, (8, 20, 0)$ from point $A\, (0, 5, 12)$,the particle moves on paths parallel to the $x$-axis,then the $y$-axis,and then the $z$-axis. The work done by this force is ............ $J$.

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$A$ force of $F=(5 y+20) \hat{j} \, N$ acts on a particle. The work done by this force when the particle is moved from $y=0 \, m$ to $y=10 \, m$ is $... \, J.$

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When a rubber band is stretched by a distance $x$,it exerts a restoring force $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the rubber band by a distance $L$ from its unstretched position is:

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The graph between the resistive force $F$ acting on a body and the distance $x$ covered by the body is shown in the figure. The mass of the body is $25\, kg$ and the initial velocity is $2\, m/s$. When the distance covered by the body is $4\, m$,its kinetic energy would be .............. $J$.

Similar Questions

The figure shows the relationship between force and position. What is the work done by the force for the displacement of the object from $x = 1 \; cm$ to $x = 5 \; cm$ in ergs?

What will be the area under the graph of variable force versus position?

The components of a force acting on a particle vary according to the graphs shown. To reach point $B\, (8, 20, 0)$ from point $A\, (0, 5, 12)$,the particle moves on paths parallel to the $x$-axis,then the $y$-axis,and then the $z$-axis. The work done by this force is ............ $J$.

$A$ force of $F=(5 y+20) \hat{j} \, N$ acts on a particle. The work done by this force when the particle is moved from $y=0 \, m$ to $y=10 \, m$ is $... \, J.$

When a rubber band is stretched by a distance $x$,it exerts a restoring force $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the rubber band by a distance $L$ from its unstretched position is:

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