SATHEE: Laws of Motion 3 Question 18

Laws of Motion 3 Question 18

19. Two blocks $A$ and $B$ of equal masses are released from an inclined plane of inclination $45^{\circ}$ at $t = 0$ . Both the blocks are initially at rest. The coefficient of kinetic

friction between the block $A$ and the inclined plane is 0.2 while it is 0.3 for block $B$ . Initially the block $A$ is $\sqrt{2} m$ behind the block $B$ . When and where their front faces will come in a line?

(Take $g = 10 m / s^{2}$ )

(2004, 5M)

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Answer:

Correct Answer: 19. $s_{A} = 8 \sqrt{2} m, 2 s$

Solution:

Acceleration of $A$ down the plane,

$\begin{aligned} a_{A} & = g \sin 45^{\circ} - μ_{A} g \cos 45^{\circ} \\ = (10) \frac{1}{\sqrt{2}} - (0.2) (10) \frac{1}{\sqrt{2}} = 4 \sqrt{2} m / s^{2} \end{aligned}$

Similarly acceleration of $B$ down the plane,

$\begin{aligned} a_{B} & = g \sin 45^{\circ} - μ_{B} g \cos 45^{\circ} \\ = (10) \frac{1}{\sqrt{2}} - (0.3) (10) \frac{1}{\sqrt{2}} = 3.5 \sqrt{2} m / s^{2} \end{aligned}$

The front face of $A$ and $B$ will come in a line when,

$or \begin{aligned} s_{A} & = s_{B} + \sqrt{2} \\ \frac{1}{2} a_{A} t^{2} & = \frac{1}{2} a_{B} t^{2} + \sqrt{2} \\ \frac{1}{2} \times 4 \sqrt{2} \times t^{2} & = \frac{1}{2} \times 3.5 \sqrt{2} \times t^{2} + \sqrt{2} \end{aligned}$

Solving this equation, we get $t = 2 s$

Further, $s_{A} = \frac{1}{2} a_{A} t^{2} = \frac{1}{2} \times 4 \sqrt{2} \times (2)^{2} = 8 \sqrt{2} m$

Hence, both the blocks will come in a line after $A$ has travelled a distance $8 \sqrt{2} m$ down the plane.

Laws of Motion 3 Question 18

19. Two blocks $A$ and $B$ of equal masses are released from an inclined plane of inclination $45^{\circ}$ at $t = 0$ . Both the blocks are initially at rest. The coefficient of kinetic

Answer:

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Laws of Motion 3 Question 18

19. Two blocks A and B of equal masses are released from an inclined plane of inclination 45∘ at t=0. Both the blocks are initially at rest. The coefficient of kinetic

Answer:

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19. Two blocks $A$ and $B$ of equal masses are released from an inclined plane of inclination $45^{\circ}$ at $t = 0$ . Both the blocks are initially at rest. The coefficient of kinetic