Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure- The breaking stress of the metal is 2 - 109 N m -2- What should be the minimum radius of the wire used if it is not to break- Take g -10 ms -2-A- 2-3 - 10-5 mB- 4-6 - 10-4 mC- 4-6 - 10-5 mD- 2-3 - 10-4 m

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Byju's Answer

Standard XII

Physics

Longitudinal Stress

Two blocks of...

Question

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $2 \times 10^{9} N m^{- 2}$ . What should be the minimum radius of the wire used if it is not to break? Take $g = 10 m s^{- 2}$ .

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Solution

The correct option is C

The stress in the wire = $\frac{T e n s i o n}{A r e a o f c r o s s s e c t i o n}$
To avoid breaking, this stress should not exceed the breaking stress.
Let the tension in the wire be T. The equations of motion of the two blocks are,
T - 10 N = (1 kg)a
And 20 N - T = (2kg) a.
Eliminating a from these equations,
$T = (\frac{40}{3}) N$

The breaking stress = $\frac{T}{π r^{2}}$

If the minimum radius needed to avoid breaking is r,

Solving this,
$r = 4.6 \times 10^{- 5} m$

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Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is 2×109Nm−2. What should be the minimum radius of the wire used if it is not to break? Take g=10ms−2.

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $2 \times 10^{9} N m^{- 2}$ . What should be the minimum radius of the wire used if it is not to break? Take $g = 10 m s^{- 2}$ .