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Can someone explain A small mass attached to a string rotates on frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the cutcular motion to decrease by a factor of 2, the kinetic enee

A small mass attached to a string rotates on frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the cutcular motion to decrease by a factor of 2, the kinetic eneegy of the mass will

  • Option 1)

    remain constant

  • Option 2)

    increase by a factor of 2

  • Option 3)

    increase by a factor of 4

  • Option 4)

    decrease by a factor of 2

 
Answers (1)
309 Views
V Vakul

As discussed in

Angular momentum -

vec{L}=vec{r}	imes vec{p}

- wherein

vec{L}  represent angular momentum of a moving particle about a point.

it can be calculated  as L=r_1, P=r, P_1

r_1 = Length of perpendicular on line of motion

P_1 = component of momentum along perpendicualar to r

 

K=\frac{L^{2}}{2I}=\frac{L^{2}}{2mr^{2}}

K'=\frac{L^{2}}{2m \frac{r^{2}}{4}}=\frac{4L^{2}}{2mr^{2}}

\frac{K'}{K}=4\:\:\:\:\:\Rightarrow K'=4K

\therefore K.\varepsilon is increased by a factor of 4 


Option 1)

remain constant

This option is incorrect.

Option 2)

increase by a factor of 2

This option is incorrect.

Option 3)

increase by a factor of 4

This option is correct.

Option 4)

decrease by a factor of 2

This option is incorrect.

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