Question

A body is displaced from position $A$ to position $B$. Kinetic and potential energies of the body at positions $A$ and $B$ are $K_A=70\text{J},U_A=-50\text{J},K_B=-20\text{J}$ and $U_B=30\text{J}$. Then:

• A. Work done by conservative forces is $-80\text{J}$.
• B. Work done by all the forces is $-90\text{J}$.
• C. Work done by non-conservative forces is $-10\text{J}$.
• D. Work done by all the forces is $-80\text{J}$.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Work done by conservative forces is $-80\text{J}$.
B Work done by all the forces is $-90\text{J}$.
C Work done by non-conservative forces is $-10\text{J}$.

Work done due to conservative force $=-$ (Change in P.E.)
$\Rightarrow W_c=-\Delta U$
$\Rightarrow W_c=-(U_B-U_A)$
$\Rightarrow W_c=-(30-(-50)$
$\Rightarrow W_c=-80\text{J}$
Work done by all forces = change in K.E.
$\Rightarrow W_{all}=K_B-K_A$
$\Rightarrow W_{all}=-20-70$
$\Rightarrow W_{all}=-90\text{J}$
Let $W_{nc}$ be the work done by the other (non-conservative) forces.
$W_{all}=-90\text{J}$
$\Rightarrow W_c+W_{nc}=-90$
$\Rightarrow -80+W_{nc}=-90$
$\Rightarrow W_{nc}=-90+80$
$\Rightarrow W_{nc}=-10\text{J}$
Hence, options $\left(a\right)$, $\left(b\right)$ and $\left(c\right)$ are correct.