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Standard XII

Physics

Problems with Pseudo Force

A block of ma...

Question

A block of mass $m_{1} = 1 k g$ another mass $m_{2} = 2 k g$ , are placed together (see figure) on an inclined plane with angle of inclination $θ$ . Various values of $θ$ are given in List I. The coefficient of friction between the block $m_{1}$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_{2}$ and the plane are equal to $μ = 0.3$ . In List II expressions for the friction on the block $m_{2}$ are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option.
The acceleration due to gravity is denoted by g.
[Useful information: $t a n ({5.5}^{\circ}) \approx 0.1; t a n ({11.5}^{\circ}) \approx 0.2; t a n ({16.5}^{\circ}) \approx 0.3]$

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Solution

Condition for net sliding,
$f_{m a x} > (m_{1} + m_{2}) g s i n θ$
$μ N > (m_{1} + m_{2}) g s i n θ$
$0.3 m_{2} g c o s θ \geq 30 s i n θ$
$6 \geq 30 t a n θ$
$1 / 5 \geq t a n θ$
$0.2 \geq t a n θ$
$∴$ for P, Q
$f = (m_{1} + m_{2}) g s i n θ$
For r and S
$f = f_{m a x} = μ m_{2} g s i n θ$

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Condition for net sliding,fmax>(m1+m2)gsinθμN>(m1+m2)gsinθ0.3m2gcosθ≥30sinθ6≥30tanθ1/5≥tanθ0.2≥tanθ∴ for P, Qf=(m1+m2)gsinθFor r and Sf=fmax=μm2gsinθ