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Ladder has its long $2.5\,m$ and weight $150\,N$ at its center of gravity $1\,m$ from the bottom. Weight of $ 40$ Nische at the top end. Find out the work required to raise the ladder from horizontal position to vertical position, if the linear momentum is increased by $50\% $. At what percentage of kinetic energy will increase? Thrice the momentum fobbed:

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Last updated date: 17th Jul 2024
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Answer
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Hint:Work is done only when some force is applied on the object or body.Using the work done formula only we are going to calculate the given data. For calculating total work done first of all we have to split the work into two equal forms. From this only we are calculating the total work.

Complete step by step answer:
Work is said to be done when an object experiences some force.
Work done formula $W = F \times d$
Whereas, $F$ is work done by kinetic force and $d$ is displacement of magnitude.
Given that,
Weight of the ladder, W=$150\,N$
Height of the ladder, h=$2.5\,m$
Additional weight added at the top of the ladder = $40\,N$
Center of gravity =$1\,m$

Work done by the ladder, when raised to the height,
${W_1}$=weight $ \times $center of gravity
${W_1}= 150 \times 1 \\
\Rightarrow {W_1}= 150 \\ $
When the work done by the ladder, raised to $2.5\,m$ long
${W_2} = 2.5 \times 40 \\
\Rightarrow {W_2}= 100\,J \\$
Total work done by the ladder,
$W = {W_1} + {W_2} \\
\Rightarrow W= 150 + 100 \\
\therefore W= 250\,J \\$
The total work required by the ladder to raise from horizontal to vertical position raised by $50\% $ of linear momentum is $250j$

Additional information:
Kinetic energy is directly proportional to mass of the object and to its square. Kinetic energy can be measured in kilograms meters per second. Theoretically center of gravity is where the total body weight is thought to be concentrated.

Note:Center of gravity is identical to center of mass.Linear momentum is directly proportional to the mass and its velocity. It ties momentum and velocity in one quantity. Work to be done when an object experiences displacement. The S.I unit of work is measured in joules (J).