Question

Calculate the acceleration 'a' of the system and the tensions Ti and T2 in the
strings as shown in figure 1. (Assume that the table and the pulleys are
frictionless and the string is massless and inextensible).
​

Answer 1

Answer:

a = g / 9 m / s²

T₁ = 30g / 9 N

T₂ = 40g / 9 N

Explanation:

To find ---> Value of tension T₁ and T₂ in the strings respectively and acceleration of the system.

Solution---> We know that,

Force = mass × acceleration

Now,

For object whose mass is 5 kg

Weight of 5 kg mass = 5 g Newton

Forces on 5kg mass object are 5g N downwards and T₂ N upward , but object moves downward so,

Force applied on object = 5g - T₂

Force = mass × acceleration

=> 5g - T₂ = 5 a ...............( 1 )

Now For 3kg mass object forces are 3g N downward and T₁ upward but object moves upward , so,

T₁ - 3g = 3a ......................( 2 )

For object of 10 Kg mass,

Forces in horizontal directions are T₂ in right direction and T₁ in Left direction and object moves in right direction so,

T₂ - T₁ = 10 a ........................ ( 3 )

adding ( 1 ) , ( 2 ) and ( 3 ) , we get,

5g - T₂ + T₁ - 3g + T₂ - T₁ = 5a + 3a + 10a

=> 2g = 18a

=> a = 2g / 18

=> a = g / 9

Putting a = g / 9 in equation ( 1 )

=> 5g - T₂ = 5 ( g / 9 )

=> 5g - ( 5g / 9 ) = T₂

=> T₂ = ( 45g - 5g ) / 9

=> T₂ = 40g / 9 N

Putting a = g / 9 in equation ( 2 )

=> T₁ - 3g = 3 ( g / 9 )

=> T₁ = 3g + ( 3g / 9 )

=> T₁ = 30g / 9 N