Question

The coefficient of kinetic friction is 0.03 in the diagram where mass $m _ { 2 } = 20 \mathrm {~kg}$ and $m _ { 1 } = 4 \mathrm {~kg}$ . The acceleration of the block shall be $\left( g = 10 m s ^ { - 2 } \right)$

• A. 1.8 $m s ^ { - 2 }$
• B. 0.8 $m s ^ { - 2 }$
• C. 1.4 $m s ^ { - 2 }$
• D. 0.4 $m s ^ { - 2 }$ Q

Answer 1

Answer: (C)

1.4 $m s ^ { - 2 }$

Answer 2

Let the acceleration of the system is a

From the F.B.D. of $m _ { 2 }$

$T - F = m _ { 2 } a$ ⇒ $T - \mu m _ { 2 } g = m _ { 2 } a$

⇒ $T - 0.03 \times 20 \times 10 = 20 a$ ⇒ $T - 6 = 20 a$ .....(i)

From the FBD of $m _ { 1 }$

$m _ { 1 } g - T = m _ { 1 } a$

⇒ $4 \times 10 - T = 4 a$ ⇒ $40 - T = 4 a$ ...(ii)

Solving (i) and (ii) $a = 1.4 m / s ^ { 2 }$