## Numericals based on blocks on smooth surface

Question 1:

Find the acceleration of 6kg,4kg,10kg block ? It is assumed that all susfaces are friction less and smooth.(a) 18 m/s², 12 m/s², 30 m/s²

(b) 18 m/s², 30 m/s², 12 m/s²

(c) 12 m/s², 18 m/s², 30 m/s²

(d) None of these

**Solution:**
Total mass of system :M= 6+4+10=20Kg

Net force on the system :F= 100-40=60N

Acceleration of system: 60/20=3 m/s²

Force on 6kg block =6*3=18N

Force on 4kg block =4*3=12N

Force on 6kg block =10*3=30N

Question 2:

Find the acceleration of each block?It is assumed that both block are palced on friction less surface.(a) 10 m/s²

(b) 10/3 m/s²

(c) 3 m/s²

(d) None of these

**Solution: **
Total mass of system :M= 2+4=6Kg

Net force on the system :F=20N

Acceleration of system: 20/6=10/3 m/s²

**Solution: **

Case1:

Total mass of system :M= 1+2=Kg

Net force on the system :F=6N

Acceleration of system: 6/3=2 m/s²

Let contact force between the block= N1

6-N1=1*2

NI=6-2=4N

Case2:

Total mass of system :M= 1+2=Kg

Net force on the system :F=6N

Acceleration of system: 6/3=2 m/s²

Let contact force between the block= N2

6-N2=2*2

N2=6-4=2N

Ratio of reaction forces

N1:N2=4/2=2:1

**Solution: **

Question 5:

Two blocks A and B wach mass m each are paced on smooth horizontal surface.Two forces F and 2F are applied on the block A nad B respectively as shown in figure below.The block A doenot slide over on block B at contact surface.What would be the normal reaction N between the blocks.(a) N=3F/2

(b) N=F/3

(c) N=3F

(d) None of these

**Solution:**

Question 6:

Rigid blocks are kept in contact on a frictionless surface as shown in figure .What would be contact forces between A&B and contact force between B&C.(a) 110N,80N

(b) 120N,80N

(c) 130N,80N

(d) None of these

**Solution:**

Fnet= (200cos37°)-(100cos53°)

Fnet= (200*4/5)-(100*3/5)

Fnet=160-60 =100N

Total mass of system=10+6+4=20Kg

a= 100/20=5m/s²

Calculation of contact forces between A & B:

FBD of block A

160-R1=10*5

R1=160-50=110N

Calculation of contact forces between B & C:

FBD of block B

110-R2=6*5

R2=110-30=80N

Question 7:

Find the contact force between block 4Kg and 2KG mass?(a) 0N

(b) 4N

(c) 7N

(d) None of these

**Solution:**

Question 8:

Rigid blocks are kept in contact on a frictionless surface as shown in figure .What would be contact forces between A&B and contact force between B&C.(a) 40N,20N

(b) 50N,20N

(c) 60N,20N

(d) None of these

**Solution:**
Fnet=100-(5+3+2)gsin37°

Fnet=100-10*10*3/5

Fnet=100-60 =40N

Total mass of system=5+3+2=10Kg

a= 40/10=4m/s²

Calculation of contact forces between A & B:

Calculation of contact forces between B & C:

Question 9:

Three blocks A,B and C masses 4Kg,2Kg and 1Kg respectively are in contact on a smooth surface as shown fig. below A force of 14 N is applied on 4Kg block What would be contact force between A & B.(a) 4N

(b) 5N

(c) 6N

(d) None of these

**Solution:**
Fnet=14N

Total mass of system=4+2+1=7Kg

a=14/7=2m/s²

Let contact force between A & B.

14-R=4*2

R=14-8=6N