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A heavy body of mass 25kg is to be dragg...

A heavy body of mass `25kg` is to be dragged along a horizontal plane (`mu` = `(1)/(sqrt(3))`. The least force required is `(1 kgf = 9.8 N)`

A

25 kgf

B

2.5 kgf

C

12.5 kgf

D

6.25 kgf

Text Solution

Verified by Experts

The correct Answer is:
C
Angle of friction `theta=tan^(-1)(mu)`
or `theta=tan^(-1)((1)/(sqrt(3)))=30^(@)`

Suppose the body is dragged by a
force F acting at an angle `alpha` with
horizontal. Then ,
N=mg-F sin `alpha`
and
F cos `alpha`= `mu N=mu(mg-F sin alpha)`
`therefore F=(mu mg)/(cos alpha+mu sin alpha)`
`F_("min")=(mu mg)/(sqrt(1+mu^(2)))=((1/sqrt(3))(25)(g))/(sqrt(1+(1)/(3)))`
= 12.5 g
12.3 kgf
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