Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Consider the Situation Shown in the Following Figure. Calculate (A) the Acceleration of the - Physics

Sum

Consider the situation shown in the following figure. Calculate (a) the acceleration of the 1.0 kg blocks, (b) the tension in the string connecting the 1.0 kg blocks and (c) the tension in the string attached to 0.50 kg.

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Solution


From the above diagrams:
T + ma − mg = 0
T + 0.5a − 0.5 g = 0                       (1)
μR + ma + T1 − T = 0
μR + 1a + T1 − T = 0                      (2)
μR + 1a − T1 = 0
μR + a = T1                                    (3)
From Equations (2) and (3) we have
μR + a = T − T1
⇒ T − T1 = T1
⇒ T = 2T1
So, Equation (2) becomes
μR + a + T1 − 2T1 = 0
⇒ μR + a − T1 = 0
⇒ T1 = μR + a
        = 0.2g + a                       (4)

and Equation (1) becomes
2T1 + 0.5a − 0.5g = 0
`=> T_1=(0.5g-0.5a)/2`
= 0.25g - 0.25a                    (5)
From Equations (4) and (5)
0.2g + a = 0.25g − 0.25a
`=>a=0.05/1.25xx10`
= 0.4 x 10 m/s2                     [g = 10 m/s2]
Therefore,
(a) the acceleration of each 1 kg block is 0.4 m/s2,
(b) the tension in the string connecting the 1 kg blocks is
   T1 = 0.2g + a + 0.4 = 2.4 N
ā€‹    and
(c) the tension in the string attached to the 0.5 kg block is 
    T = 0.5g − 0.5a
       = 0.5 × 10 − 0.5 × 0.4
       = 4.8 N.

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 6 Friction
Exercise | Q 11 | Page 97
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