A body of mass 10kg on a smooth inclined plane is connected to a smooth pulley to a mass of 15kg as shown above, the acceleration of the system is

Physics Jamb, Waec, Neco Past Questions & Answers on FRICTIONAL FORCE

QUESTIONS 11: A body of mass 10kg on a smooth inclined plane is connected to a smooth pulley to a mass of 15kg as shown above, the acceleration of the system is

A. 1/4g

B. 8/25g

C. 1/2g

D. 2/5g

E. 3/4g

SOLUTIONS 

Let M1 = 10kg; and M2 = 15kg respectively.

M1 = 10kg is inclined at an angle of 30° 

g=10m/s²

Hence, Force F, = mg 

but when the mass is inclined at an angle, 

Force F, = mgsinθ

The product of "total mass" and acceleration equals the Force (F = ma)

=>> Note that M2 and M1 are acting to oppose each other due to the pulley in 

between them.erefore, 

Fr = P - F

m x a = ma - ma

(M1+M2)a = M2g - M1gsinθ

(10+15)a=15g-10gsin30

25a=10g

a=10g/25

a=2/5g

OR

Considering the pulley system, 

=>>> for mass 10kg;

F=T-mgsin30

(f=ma and T represents the tension in the string)

Therefore, 

ma=T-mgsin30

10a=T-5g .............. eq. 1

=>>> for mass 15kg,

F=mg-T (the weight is 

not acting on the inclined plane)

ma=mg -T

15a=-T+15g ........... eq. 2

Solving the two eq(s) simultaneously, and eliminating tension to get a;

10a=T-5g

15a=-T+15g

25a=10g (divide through by 25)

a= ⅖g