Answer
Verified
91.2k+ views
Hint: When the block is being brought down by the chain; two forces are acting on it. The force applied by the chain and the gravitational attraction are acting in opposite directions therefore both forces are doing some work on the block. The work done by the chain is equal to the difference in total work done on the block and work done by gravity.
Formulas Used:
\[E=W=\dfrac{1}{2}m{{v}^{2}}\]
\[\text{The work is done by the chain on the block} = \text{Total energy}- \text{Work done by gravity} \]
Complete step-by-step solution
A block of mass \[30\,kg\] held by a chain is moving down with velocity \[40\,cm\,{{s}^{-1}}=0.4m{{s}^{-1}}\]
Therefore the total work done on the block is –
\[E=W=\dfrac{1}{2}m{{v}^{2}}\]
Here, \[m\] is the mass of the block
\[v\] is the velocity of the block
Substituting values in the above equation, we get,
\[W=\dfrac{1}{2}\times 30\times {{(0.4)}^{2}}\]
\[\Rightarrow W=2.4J\] - (1)
Therefore the total work done on the block is \[2.4J\]
The work done on the block by the gravity is given by-
\[{{W}_{g}}=mgh\]
Here, \[g\] is acceleration due to gravity
\[h\] is the height through which it was brought down
Therefore,
\[\begin{align}
& {{W}_{g}}=30kg\times 10ms{}^{-2}\times 2m \\
& {{W}_{g}}=600J \\
\end{align}\]
\[\text{The work is done by the chain on the block} = \text{Total energy}- \text{Work done by gravity} \]
\[\begin{align}
& {{W}_{c}}=W-{{W}_{g}} \\
& {{W}_{c}}=2.4-600 \\
& {{W}_{c}}=-597.6J \\
\end{align}\]
The work done by the chain is \[-597.6J\], therefore the correct option is (C).
Note: When work done is negative, the work is being done on the system. When work is done is positive, the work is being done by the system. Work done by gravity is defined as the work done to take an object up to a height \[h\]. When the block is coming down, its potential energy is converted to kinetic energy.
Formulas Used:
\[E=W=\dfrac{1}{2}m{{v}^{2}}\]
\[\text{The work is done by the chain on the block} = \text{Total energy}- \text{Work done by gravity} \]
Complete step-by-step solution
A block of mass \[30\,kg\] held by a chain is moving down with velocity \[40\,cm\,{{s}^{-1}}=0.4m{{s}^{-1}}\]
Therefore the total work done on the block is –
\[E=W=\dfrac{1}{2}m{{v}^{2}}\]
Here, \[m\] is the mass of the block
\[v\] is the velocity of the block
Substituting values in the above equation, we get,
\[W=\dfrac{1}{2}\times 30\times {{(0.4)}^{2}}\]
\[\Rightarrow W=2.4J\] - (1)
Therefore the total work done on the block is \[2.4J\]
The work done on the block by the gravity is given by-
\[{{W}_{g}}=mgh\]
Here, \[g\] is acceleration due to gravity
\[h\] is the height through which it was brought down
Therefore,
\[\begin{align}
& {{W}_{g}}=30kg\times 10ms{}^{-2}\times 2m \\
& {{W}_{g}}=600J \\
\end{align}\]
\[\text{The work is done by the chain on the block} = \text{Total energy}- \text{Work done by gravity} \]
\[\begin{align}
& {{W}_{c}}=W-{{W}_{g}} \\
& {{W}_{c}}=2.4-600 \\
& {{W}_{c}}=-597.6J \\
\end{align}\]
The work done by the chain is \[-597.6J\], therefore the correct option is (C).
Note: When work done is negative, the work is being done on the system. When work is done is positive, the work is being done by the system. Work done by gravity is defined as the work done to take an object up to a height \[h\]. When the block is coming down, its potential energy is converted to kinetic energy.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
Velocity of car at t 0 is u moves with a constant acceleration class 11 physics JEE_Main