Home
Class 11
PHYSICS
An object has a displacement from positi...

An object has a displacement from position vector `vec(r_(1))=(2hat(i)+3hat(j))m" to" " "vecr_(2)=(4hat(i)+hat(j))` m under a force `vec(F)=(3x^(2)i+2yhat(j))N`, Find the work done by this force.

Text Solution

Verified by Experts

`W = int_(vec(r )_(i))^(vec(r )_(f))vec(F).dvec(r )=int_(vec(r )_(1))^(vec(r )_(2))(3x^(2)hat(i)+2y hat(j)).(dxhat(i)+dyhat(j)+dzhat(k))`
`= int_(2)^(4)3x^(2)dx+int_(3)^(6)2y dy=[x^(3)]_(2)^(4)+[y^(2)]_(3)^(6)=83J`
Promotional Banner

Similar Questions

Explore conceptually related problems

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Work done by a force F on a body is W = F .s, where s is the displacement of body. Given that under a force F = (2 hat i +3 hat j +4 hat k) N a body is displaced from position vector r_1 = (2 hat i +3 hat j + hat k) m to the position vector r_2 = (hat i +hat j+ hat k) m. Find the work done by this force.

Work done by a force F on a body is W = F .s, where s is the displacement of body. Given that under a force F = (2 hat I +3 hat j +4 hat k) N a body is displaced from position vector r_1 = (2 hat I +3 hat j + hat k) m to the position vector r_2 = (hat i +hat j+ hat k) m. Find the work done by this force.

A force vec(F)=2hat(i)-3hat(j)+7hat(k) (N) acts on a particle which undergoes a displacement vec(r )=7hat(j)+3hat(j)-2hat(k)(m) . Calculate the work done by the force.

Find the scalar and vector products of two vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)) and vec(b)= (hat(i)-2hat(j)+3hat(k)) .

Find the dot product of two vectors vec(A)=3hat(i)+2hat(j)-4hat(k) and vec(B)=2hat(i)-3hat(j)-6hat(k) .

Find the angle between the vector vec(a) =2 hat(i) + 3hat(j) - 4 hat(k) and vec(b) = 4hat(i) +5 hat(j) - 2hat(k) .

A unit vector in the dirction of resultant vector of vec(A)= -2hat(i)+3hat(j)+hat(k) and vec(B)= hat(i)+2hat(j)-4hat(k) is

Find a vector perpendicular to vector vec(A)=(hat(i)+2hat(j)-3hat(k)) as well as vec(B)=(hat(i)+hat(j)-hat(k))

Find the scalar and vector products of two vectors vec(A)=(3hat(i)-4hat(j)+5hat(k)) "and" vec(B)=(-2hat(i)+hat(j)-3hat(k)) .