Question

A block hangs freely from the end of a spring. A boy then slowly pushes the block upwards so that the spring becomes strain free. The gain in gravitational potential energy of the block during this process is not equal to

• A. The work done by the boy against the gravitational force acting on the block
• B. The loss of energy stored in the spring minus the work done by the tension in the spring.
• C. The work done on the block by the boy plus the loss of energy stored in the spring
• D. The work done on the block by the boy minus the work done by the tension in the spring plus the loss of energy stored in the spring
• E. The work done on the block by the boy minus the work done by the tension in the spring

Answer 1

Answer: (A), (B), (D), (E)

The correct options are
A The work done by the boy against the gravitational force acting on the block
B The loss of energy stored in the spring minus the work done by the tension in the spring.
D The work done on the block by the boy minus the work done by the tension in the spring plus the loss of energy stored in the spring
E The work done on the block by the boy minus the work done by the tension in the spring

let $x_0$ be the initial extension in the spring

Initial energy stored in the spring = $\frac{1}{2}k{x_0}^2$

potential energy gained by the mass = $mg{x}_0$

work is done against gravity and towards spring force

so work done increases gravitational potential energy and decreases spring's potential energy

total energy gained = $mg{x}_0-\frac{1}{2}k{x_0}^2$

let work done by boy = $w_b$

we know that

$w_b=mg{x}_0-\frac{1}{2}k{x_0}^2$

$mg{x}_0=w_b+\frac{1}{2}k{x_0}^2$

$optionCiscorrectotheroptionsarewrong$