Question

Two blocks are connected by a string and kept on the frictionless surface as shown in the figure. Block 2 is pulled by a force of 40 N, which accelerates both the blocks at 3m/s2. Calculate the tension in the string connecting the blocks if the mass of both the blocks are the same.

A.)120 N
B.).80 N
C.)40 N
D.)20 N
E.)13 N

Answer 1

Hint: Firstly, make the free body diagram or find out forces acting on block 1 and block 2. Thereafter apply the tension force formula and balance the force equations. Now solve the equations and get the value of required tension.

Complete step by step answer:
Given that the surface is frictionless and the mass of both the blocks are the same. So FBD for both will be as shown below:

Therefore, applying tension force formula and balancing the equations,

\[T=ma\] --------(1)

and,

\[F-T=ma\]
i.e., \[40-T=ma\] --------(2)

On comparing equation (1) and (2),

\[T=40-T\]
\[2T=40\]
\[T=\dfrac{40}{2}\]
\[T=20N\]

Therefore, the tension in the string connecting the blocks will be 20 N
Hence, the correct option is D, i.e., 20 N

Additional Information:
(I)Tension force problems can be solved easily by keeping following steps in mind.
(II)Problem restatement
(III)Think and guess about what is happening there
(IV)Diagrams & Variables
(V)Free Body Diagrams & Equations
(VI)Solution

Note: Students should be very careful in making free body diagrams and in writing force equations while solving tension force problems. Students should follow step by step procedure as described in additional information for avoiding errors and also be attentive in solving force equations finally.