Question

An object is displaced from point $A(0,1,2)m$ to a point $B(1,2,3)m$ under the influence of a force $\overrightarrow{F}=2x\hat{i}+3y^2\hat{j}+\hat{k}.$ The workdone by this force is

• A. $-10\text{J}$
• B. $12\text{J}$
• C. $9\text{J}$
• D. $0\text{J}$

Answer 1

The correct option is C $9\text{J}$

Given variable force $\overrightarrow{F}=2x\hat{i}+3y^2\hat{j}+\hat{k}$
Displacement vector $\overrightarrow{ds}=dx\hat{i}+dy\hat{j}+dz\hat{k}$
workdone $\left(W\right)=\int \overrightarrow{F}.\overrightarrow{ds}={\int }_{(0,1,2)}^{(1,2,3)}(2x\hat{i}+3y^2\hat{j}+\hat{k}).(dx\hat{i}+dy\hat{j}+dz\hat{k})$$W={\int }_{(0,1,2)}^{(1,2,3)}2xdx+3y^{2}dy+dzW=x^2{|}_{\left(0\right)}^{\left(1\right)}+y^3{|}_{\left(1\right)}^{\left(2\right)}+z{|}_{\left(2\right)}^{\left(3\right)}$$=1+(2^3-1^3)+(3-2)=1+7+1=9\text{J}$