5
Question
Assume that a body is displaced from −→rA=(2 m,4 m,−6 m) to −→rB=(6^i−4^j+2^k) m, under a constant force →F=(2^i+3^j−^k) N. Calculate work done by the force.
Assume that a body is displaced from −→rA=(2 m,4 m,−6 m) to −→rB=(6^i−4^j+2^k) m, under a constant force →F=(2^i+3^j−^k) N. Calculate work done by the force.
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Solution
The correct option is C −24 J
The work done by the constant force →F during displacement →S of a particle is scalar product of force and displacement and is given by
W=→F.→S
−→rA=(2^i+4^j−6^k) m, −→rB=(6^i−4^j+2^k) m
→S=−→rB−−→rA
=(6^i−4^j+2^k)−(2^i+4^j−6^k)=4^i−8^j+8^k
W=→F.→S=(2^i+3^j−^k).(4^i−8^j+8^k)=8−24−8=−24 J
Hence option C is the correct answer
The work done by the constant force →F during displacement →S of a particle is scalar product of force and displacement and is given by
W=→F.→S
−→rA=(2^i+4^j−6^k) m, −→rB=(6^i−4^j+2^k) m
→S=−→rB−−→rA
=(6^i−4^j+2^k)−(2^i+4^j−6^k)=4^i−8^j+8^k
W=→F.→S=(2^i+3^j−^k).(4^i−8^j+8^k)=8−24−8=−24 J
Hence option C is the correct answer
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