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Question
A man stands on a spring balance in a lift. At some instant, he finds that the scale reading has changed from 60N to 50N for a while and then comes back to the original mark. What should he conclude?
A man stands on a spring balance in a lift. At some instant, he finds that the scale reading has changed from 60N to 50N for a while and then comes back to the original mark. What should he conclude?
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Solution
The correct option is C The lift while in constant motion upwards, suddenly stopped
If the reading of the spring scale, i.e., apparent weight of the person moving in a lift, decreases, the formula for reaction, R must be m(g−a), there are only two possibilities for this,(i) the normal situation in which this equation is valid, the accelerated motion of the lift is downwards(ii) During upward accelerated motion of the lift, the equation of reaction i.e. apparent weight is m(g+a). If the upward motion is retarded, acceleration is negative.The equation for upward motion also becomes m(g−a). Now, it is given that the scale reading suddenly changes from 60N to 50N for a moment and then comes back to the 60N mark. It means that for most of the journey, since the reading is constant, the lift must have been in motion with uniform velocity either upwards or downwards. If in the downward motion with constant velocity, when there is a sudden retardation, the equation of reaction will become m(g+a). In that case the reading should momentarily increase. In the upward motion with constant velocity, for a sudden retardation, the equation of reaction will become m(g-a) and the reading of the scale will consequently decrease. Once the lift comes to rest in either of the case, the reaction will be same as that in the case of constant velocity motion i.e., mg.As we know the spring scale gives the measure of the normal force exerted from the surface of the lift.Given the reading decreased from 60N to 50N.Hence, the normal force has decreased from mg to m(g-a) which is possible when the lift, going constantly upwards, suddenly stops.
If the reading of the spring scale, i.e., apparent weight of the person moving in a lift, decreases, the formula for reaction, R must be m(g−a), there are only two possibilities for this,
(i) the normal situation in which this equation is valid, the accelerated motion of the lift is downwards
(ii) During upward accelerated motion of the lift, the equation of reaction i.e. apparent weight is m(g+a). If the upward motion is retarded, acceleration is negative.
The equation for upward motion also becomes m(g−a). Now, it is given that the scale reading suddenly changes from 60N to 50N for a moment and then comes back to the 60N mark. It means that for most of the journey, since the reading is constant, the lift must have been in motion with uniform velocity either upwards or downwards.
If in the downward motion with constant velocity, when there is a sudden retardation, the equation of reaction will become m(g+a). In that case the reading should momentarily increase.
In the upward motion with constant velocity, for a sudden retardation, the equation of reaction will become m(g-a) and the reading of the scale will consequently decrease.
Once the lift comes to rest in either of the case, the reaction will be same as that in the case of constant velocity motion i.e., mg.
As we know the spring scale gives the measure of the normal force exerted from the surface of the lift.
Given the reading decreased from 60N to 50N.
Hence, the normal force has decreased from mg to m(g-a) which is possible when the lift, going constantly upwards, suddenly stops.
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