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Two wires AC and BC are tied at C of a ...

Two wires `AC` and `BC` are tied at `C` of a small sphere of mass `5kg`, which revolves at a constant speed `v` in the horizontal speed `v` in the horizontal circle of radius `1.6m`. Find the minimum value of `v`

A

(a)`4ms^(-1)`

B

(b)`2ms^(-1)`

C

(c)`2.5ms^(-1)`

D

(d)none of these

Text Solution

Verified by Experts

The correct Answer is:
A

From the force diagram shown
`T_1cos30^@+T_2cos45^@=mg`………i
`T_1sin30^@+T_2sin45^@=(mv^2)/rmg` …………..ii
From eqn i and ii it is clear that the velocity will be minimum if `T_2` is minimum (may be zero also)
`T_1/2+T_2/sqrt2=(mv^2)/r`.............iii
After solving eqn i and ii we get
`T_1=(mg-(mv^2)/r)/(((sqrt3-1)/2)`
But `T_1gt0, (mg-(mv^2)/r)/((sqrt3-1)/2)gt0`
`mggt(mv^(2))/r=gtvltsqrt(rg)`
`v_(max)=sqrt(rg)=sqrt(1.6xx10)=4m//s`
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