A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction (1/√3) . It is desired to make the body move by applying the minimum possible force F N. The value of F will be . (Round off to the Nearest Integer) [Take g=10 ms -2 ]

Question

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction (1/√3) . It is desired to make the body move by applying the minimum possible force F N. The value of F will be . (Round off to the Nearest Integer) [Take g=10 ms -2 ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/2c811941dd0e861e85a90ed505c050ce-.png" /> F cos θ=μ N F sin θ+ N = mg ⇒ F =(μ mg / cos θ+μ sin θ) F min =(μ mg /√1+μ2)=((1/√3) × 10/(2)√3)=5

Q. A body of mass $1 k g$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{3} .$ It is desired to make the body move by applying the minimum possible force $FN$ . The value of $F$ will be _________. (Round off to the Nearest Integer) [Take $g = 10 m s^{- 2}$ ]

$F cos θ = μ N$
$F sin θ + N = m g$
$\Rightarrow F = \frac{μ m g}{c o s θ + μ s i n θ}$
$F_{m i n} = \frac{μ m g}{1 + μ ^{2}} = \frac{\frac{1}{3} \times 10}{\frac{2}{3}} = 5$

Q. A body of mass 1kg rests on a horizontal floor with which it has a coefficient of static friction 3​1​. It is desired to make the body move by applying the minimum possible force FN. The value of F will be _________. (Round off to the Nearest Integer) [Take g=10ms−2 ]

Fcosθ=μN Fsinθ+N=mg ⇒F=cosθ+μsinθμmg​ Fmin​=1+μ2​μmg​=3​2​3​1​×10​=5

$F cos θ = μ N$
$F sin θ + N = m g$
$\Rightarrow F = \frac{μ m g}{c o s θ + μ s i n θ}$
$F_{m i n} = \frac{μ m g}{1 + μ ^{2}} = \frac{\frac{1}{3} \times 10}{\frac{2}{3}} = 5$