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Consider the case of two bodies of masses `m_(1) and m_(2)` which are connected by light inextensible string passing over a light smooth pulley as shown in the figure. The expression for acceleration of the system and tension of the string are expressed below under different situations:

(i) when `m_(1) gt m_(2)`. In this case
`a=((m_(1)-m_(2))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g`
(ii) when `m_(2) gt m_(1)`. In this case
`a=((m_(2)-m_(1))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g`
(iii) When `m_(1)=m_(2)=m`. In this case `a = 0, T = mg`
If `m_(1)=10kg, m_(2)=6kg and g =10m//s^(2)` then what is the acceleration of masses?

A

`2.5 m//s^(2)`

B

`5m//s^(2)`

C

`20m//s^(2)`

D

`40m//s^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`a=((m_(1)-m_(2))/(m_(1)+m_(2)))g" " T-((2m_(1)m_(2))/(m_(1)+m_(2)))g`
`a=((10-6)/(16))g=2.5m//s^(2)`
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Knowledge Check

  • Consider the case of two bodies of masses m_(1) and m_(2) which are connected by light inextensible string passing over a light smooth pulley as shown in the figure. The expression for acceleration of the system and tension of the string are expressed below under different situations: (i) when m_(1) gt m_(2) . In this case a=((m_(1)-m_(2))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g (ii) when m_(2) gt m_(1) . In this case a=((m_(2)-m_(1))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g (iii) When m_(1)=m_(2)=m . In this case a = 0, T = mg What is the tension in the string?

    A
    60N
    B
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  • Consider the case of two bodies of masses m_(1) and m_(2) which are connected by light inextensible string passing over a light smooth pulley as shown in the figure. The expression for acceleration of the system and tension of the string are expressed below under different situations: (i) when m_(1) gt m_(2) . In this case a=((m_(1)-m_(2))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g (ii) when m_(2) gt m_(1) . In this case a=((m_(2)-m_(1))/(m_(1)+m_(2)))g and T=((2m_(1)m_(2))/(m_(1)+m_(2)))g (iii) When m_(1)=m_(2)=m . In this case a = 0, T = mg If the pulley is pulled upward with acceleration equal to the acceleration due to gravity, what will be the tension in the string?

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  • Two masses m_(1) and m_(2) are connected by light inextensible string passing over a smooth pulley P . If the pulley moves vertically upwards with an acceleration equal to g then .

    A
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    B
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    The acceleration of mass `m_(1)` with respect to ground is `(3m_(2)-m_(1))/(m_(1)+m_(2))g` .
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