Question

A uniform rectangular marble slab is 3.4 m long and 2.0 m wide. It has a mass of 180 kg. If it is originally lying on the flat ground, how much work is reduced to stand it on the end?
A. 2.0 kJ
B. 3.0 J
C. 3.0 kJ
D. 3000 kJ

Answer 1

Hint: If an external force is acted on the body to move it to some distance, it is called work done. For lifting the marble slab force is applied to the center of mass of the marble slab.
The expression for the work done is
\[W=F\times h\]
W = work done
F = Force acting on the object (force acting on the centre of mass of the slab)
h = Distance moved by the object (height moved by the centre of mass of the slab)

Complete step by step answer:
Given data:
Length of the slab (l) = 3.4m
Width of the slab (b) = 2m
Mass of the rectangular slab (m) =180 kg
The slab is lifted to stand on the shorter side (b) of the marble, i.e., on 2m side. When the slab stands on Width (2m), the height of the center of mass of the slab will be at half the height of the longer side (length). i.e., centre of mass of the slab move from an height = 0 to height = \[l/2\]
Therefore,
\[h=\dfrac{l}{2}\]
Substituting value of l,
\[h=\dfrac{3.4}{2}=1.7m\]
Here, Force is \[F=mg\]
Therefore,
\[\begin{gathered}
  & W=mgh \\
 & \text{ }=180\times 9.8\times 1.7 \\
 & \text{ }=3000\text{ J} \\
\end{gathered}\]
Therefore, the total work done to make the rectangular slab stand on the shorter side is 3 kJ
The correct answer is C .

Note: The S.I unit of work is joules (J). Now, \[\text{1 kJ = 1000 J}\]. Hence, to convert joules to kilojoules, we divide the answer by 1000, that is \[\dfrac{3000\text{ J}}{1000}=3\text{ kJ}\].
If the slab stands on the longer side, i.e., on 3.4 cm, the height moved by centre of mass is half the width, that is, 1 m. Then work done will be 1.76 kJ.