A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by $x=3t-4{t}^{2}+{t}^{3}$, where x is in metres and t is in seconds. The work done during the first 4 seconds is

(1) 5.28 J

(2) 450 mJ

(3) 490 mJ

(4) 530 mJ

Concept Questions :-

Work done by variable force
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The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of 15° with the horizontal is (given: sin15°=0.2588):

(1) 4.36 kJ

(2) 5.17 kJ

(3) 8.91 kJ

(4) 9.82 kJ

Concept Questions :-

Concept of work
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A force $\stackrel{\to }{F}=5\stackrel{^}{i}+6\stackrel{^}{j}-4\stackrel{^}{k}$ acting on a body, produces a displacement $\stackrel{\to }{s}=6\stackrel{\to }{i}+5\stackrel{\to }{k}.$ Work done by the force is

(1) 18 units

(2) 15 units

(3) 12 units

(4) 10 units

Concept Questions :-

Concept of work
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A body of mass 6kg is under a force which causes displacement in it given by $S=\frac{{t}^{2}}{4}$ metres where t is time. The work done by the force in 2 seconds is-

(1) 12 J

(2) 9 J

(3) 6 J

(4) 3 J

Concept Questions :-

Work done by variable force
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A force of $\left(3\text{​\hspace{0.17em}}\stackrel{^}{i}+4\text{\hspace{0.17em}}\stackrel{^}{j}\right)$ Newton acts on a body and displaces it by $\left(3\text{\hspace{0.17em}}\stackrel{^}{i}+4\text{​}\stackrel{^}{j}\right)\text{\hspace{0.17em}}m.$ The work done by the force is

(1) 10 J

(2) 12 J

(3) 16 J

(4) 25 J

Concept Questions :-

Concept of work
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A force $\stackrel{\to }{F\text{\hspace{0.17em}}}=6\stackrel{^}{i}+2\stackrel{^}{j}-3\stackrel{^}{k}$ acts on a particle and produces a displacement of $\stackrel{\to }{s\text{\hspace{0.17em}}}=2\stackrel{^}{i}-3\stackrel{^}{j}+x\stackrel{^}{k}.$ If the work done is zero, the value of x is

(1) – 2

(2) 1/2

(3) 6

(4) 2

Concept Questions :-

Concept of work
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A particle moves from position ${\stackrel{\to }{r}}_{1}=\text{\hspace{0.17em}}3\stackrel{^}{i}+2\stackrel{^}{j}-6\stackrel{^}{k}$ to position ${\stackrel{\to }{r}}_{2}=14\stackrel{^}{i}+13\stackrel{^}{j}+9\stackrel{^}{k}$ under the action of force $4\stackrel{^}{i}+\stackrel{^}{j}+3\stackrel{^}{k}\text{\hspace{0.17em}}N.$ The work done will be

(1) 100 J

(2) 50 J

(3) 200 J

(4) 75 J

Concept Questions :-

Concept of work
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A force $\left(\stackrel{\to }{F}\right)=3\stackrel{^}{i}+c\stackrel{^}{j}+2\stackrel{^}{k}$ acting on a particle causes a displacement: $\left(\stackrel{\to }{s}\right)\text{\hspace{0.17em}}=-4\stackrel{^}{i}+2\stackrel{^}{j}+3\stackrel{^}{k}$ in its own direction. If the work done is 6 J then the value of ‘c’ is

(1) 0

(2) 1

(3) 6

(4) 12

Concept Questions :-

Concept of work
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A force $\stackrel{\to }{F}=\left(5\stackrel{^}{i}+4\stackrel{^}{j}\right)$N acts on a body and produces a displacement $\stackrel{\to }{S}=\left(6\stackrel{^}{i}-5\stackrel{^}{j}+3\stackrel{^}{k}\right)$m. The work done will be

(1) 10 J

(2) 20 J

(3) 30 J

(4) 40 J

Concept Questions :-

Concept of work
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A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table

(1) 7.2 J

(2) 3.6 J

(3) 120 J

(4) 1200 J

Concept Questions :-

Gravitational Potential energy
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Difficulty Level: