Question

A block of mass $M_1=10kg$ is placed on a slab of mass $M_2$ = 30 Kg. The slab lies on a frictionless horizontal surface as shown in figure. The coefficient of static friction between the block and slab is ${\mu }_s$ = 0.25 and that of dynamic friction is ${\mu }_k$ = 0.12. A force F = 40 N acts on block $M_1$. The acceleration of the slab will be (g = 10 m/$s^2$)

• A. 0.5 $m/s^2$
• B. 0.4 $m/s^2$
• C. 1 $m/s^2$
• D. $\frac{5}{6}m/s^2$

Answer 1

The correct option is B 0.4 $m/s^2$

Static Friction between the block is ${\mu }_k{M}_{1}g=.25\times 100=25N$

static friction < applied force

so in this case kinetic friction will be act

$f_k=.12\times 100N=12N$

FBD diagram of both the block as shown

for $M_1$ block which as acceleration $a_1$

$F-f_K=10a_1$ eq(1)..

$40-12=10a_1$

a_{1}=2.8ms^{-2}

for $M_2$ slab which as acceleration

$f_k=30a_2$ eq(2)..

$12=30a_2$

$a_2=0.4m{s}^{-2}$

solving eq(1)and eq(2)

accleration of slab is $0.4m{s}^{-2}$

Hence the B option is correct.