What is least count of an instrument?
a) The lowest value that can be measured accurately
b) The greatest value that can be measured accurately
c) Half of the lowest value that can be measured accurately
d) Mean of the lowest and highest values

Explanation

Suppose the bob is given a horizontal speed `v_0` at the bottom and it describes a complete vetical circle. Let its speed at the highest point be v. Taking the gravitatioN/Al potenial energy to be zero at the bottom the conservastion of energy gives,
`1/2 mv_0^21/2mv^2+2mgl`
or, `mv^2=mv_0^2-4mgl`.......i

The forces acting on the bob at teh highest poit are mg due to the gravity and T due to the tension in teh string. The resultant force towards the cente is therefore, `mg+T`. As the bob is moving in a circ,le, its acceleration towards the centre is `v^2/l`. Applying Newton's second law and using i,
`mg+T=mv^2/l=1/l(mv_0^2-4mgl)`
or, `mv_0^2=5mgl+Tl`
Now, for `v_0` to be minimum T should be minimum. As the minimum value of T can be zero, for minimum speed,
`mv_0^2=5mgl or, v_0=sqrt(5gl)`