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A boy measures the thickness of a human ...

A boy measures the thickness of a human hair by looking at it through a microscope of magnification 100x. After 25 observations, the boy finds that the average width of the hair in the field of view of the microscope is 3.8 mm. What is the estimate on the thickness of hair?

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To find the estimated thickness of a human hair using the data provided, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Magnification**: The microscope has a magnification of 100x. This means that the image of the hair appears 100 times larger than its actual size. 2. **Average Width in the Microscope**: The average width of the hair observed through the microscope is given as 3.8 mm. This measurement is not the actual thickness of the hair but rather the thickness as seen through the microscope. ...
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(i) A non uniform cube of side length a is kept inside a container as shown in the figure. The average density of the material of the cube is 2 rho where rho is the density of water. Water is gradually fille din the container. It is observed that the cube begins to topple, about its edge into the plane of the figure passing through pointA, when the height of the water in the container becomes (a)/(2) . Find the distance of the centre of mass of the cube from the face AB of the cube. Assume that water seeps under the cube. (ii) A rectangular concrete block (specific gravity =2.5) is used as a retatining wall in a reservoir of water. The height and width of the block are x and y respectively the height of water in the reservoir is z=(3)/(4)x . the concrete block cannot slide on the horizontal base but can rotate about an axis perpendicular to the plane of the figure and passing through point A (a) Calculate the minimum value of the ratio (y)/(x) for which the block will not begin to overturn about A. (b) Redo the above problem for the case when there is a seepage and a thin film of water is present under the block. Assume that a seal at A prevents the water from flowing out underneath the block.

When a situation demands our immediate action. It takes some time before we really respond. Reaction time is the time a person takes to observe. Think and act. For example. If a person is driving and suddenly a boy appears on the road, then the time elapsed before he slams the brakes of the car is the reaction time. Reaction time depends on complexity of the situation and on an individual. You can measure your reaction time by a simple experiment. Take a ruler and ask your friend to drop it vertically through the gap between your thumb and forefinger(Fig. 3.15). After you catch it, find the distance d travelled by the ruler. In a particular case, d was found to be 21.0 cm. Estimate reaction time.

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