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101. When a man standing on a turntable suddenly drops his hands to his height, the table moves faster. Why?

According to the law of conservation of angular momentum, "if no external torque is applied on the system then the angular momentum of that system remains constant" i.e. the system will always try to keep the angular momentum conserved (). By dropping the hands, the moment of inertia I will be decreased. In the absence of external torque, the angular velocity must increase. Hence, when a man standing on a turntable suddenly drops his hands to his height, the table moves faster.

 

102. Which wrench are more useful-a wrenches if shorter arm or those of longer arm?

If r1 & r2 be the length of the arm of longer wrench & shorter wrench respectively then t1 & t2 are respective torques observed with the same force F applied on them. Here,t1 = r1. F & t2 = r2. F. As r2 > r1 so, t2 > t1 i.e. the turning affects on the long wrench is much greater than that on the short wrench. So, the longer arm wrench is more useful.

 

 

103. A girl sits near the edge of a circular platform rotating with a uniform angular velocity . What change will be observed in the emotion of the platform?

According to the law of conservation of angular momentum, "if no external torque is applied on the system then the angular momentum of that system remains constant". The system will always tries to keep the angular momentum conserved (). In the presence of the girl, the moment of inertia I will be increased so, angular velocity  has to be decreased i.e. the platform will rotates slowly.

 

104. A helicopter has two propellers. Why?

According to the law of conservation of angular momentum, "if no external torque is applied on the system then the angular momentum of that system remains constant". The system will always tries to keep the angular momentum conserved (). If there were only one propeller, the helicopter itself would have turned in opposite direction & cannot conserve its angular momentum. In order to conserve the angular momentum, a helicopter has two propellers.

 

 

105. The bicycles have large diameter wheels. What is its important that the tyres be light weighing?

Due to large diameter wheels in the bicycles, the moment of inertia M.I. will be high though mass is small and the angular spin will be smaller. Further, if the mass is increased, more force will be required to accelerate to a given rate. Hence, bicycles have large diameter wheels and light weight.

 

 

106. The front end of the car raises little when it is accelerated rapidly, why?

The frictional force provided by the contact of the tyres of car with the ground  accelerates a car pointing forward. This exerts a torque that tends to rotate its back end down ward and its front upward. Hence, the front end of the car raises little when it is accelerated rapidly.

 
 

107. Fly wheel is used in railway engine. Why?

The flywheel is a large heavy wheel with a long cylindrical axle passing through its center of mass lying on the axis of rotation. It is constructed in such a way that most of the mass is concentrated at the rim. This increases the value of moment of inertia i.e. I. This moment of inertia opposes any change in uniform rotators. Hence, when the flywheel is attached with the engine. It assures the running of engine smoother and steadier.

 
 

108. People with long legs generally walk with a slower stride than people with short legs. Why?

Every system will try to keep the angular momentum conserved & angular momentum is given by the relation:

(where I is moment of inertia & w be the angular velocity). People with long legs generally walk with a slower stride than people with short legs. This is because short legs have less rotational inertia (i.e. I) than long legs. So, for a same angular momentum, people with long legs generally walk with a slower stride than people with short legs.

 

 

109. A disc of metal is recast in the form of a solid sphere. What will happens to the M.I. about a vertical axis passing through the center?

For the disc, the moment of inertia M.I. about a vertical axis passing through center is given by the relation:

                      

Where, M is the mass of the sphere. And for the solid sphere of same mass M, the moment of inertia M.I. about a vertical axis passing through center is given by the relation:

                      

As the radius R of the disc is always greater than that of the sphere so, the moment of inertia of disc is always greater that of the sphere. Hence, the M.I. about a vertical axis passing through the center decreases as a disc of metal recast in the form of a solid sphere.

 

 

110. Two metal sphere have same mass and same radius. If one is hollow and the other is solid, which will have greater M.I.?

As the moment of inertia M.I. of a body is given by relation I =

i.e. M.I. of a body not only depends upon the mass but also depends upon the distribution of mass from the axis of rotation. If two metal sphere have same mass and same radius but one is hollow and the other is solid, then the hollow sphere will have greater moment of inertia M.I.  because most of the mass is concentrated at large distance from the center.

 

 

111. There are two circular discs of equal masses and thickness but made of different materials. Which will have greater moment of inertia M.I. about its central axis and why?

There are two circular discs of equal masses and thickness but made of different materials. As the moment of inertia M.I. of a body is given by relation I =

i.e. M.I. of a body not only depends upon the mass but also depends upon the distribution of mass from the axis of rotation. The disc made of less dense material will have large moment of inertia M.I because the particles are at a greater distance from the axis rotation.

 

 

112. An object is tied to a string and whirled in a circular path with uniform speed. What will happen to the angular momentum of the object when the string is suddenly cut?

According to the law of conservation of angular momentum, "if no external torque is applied on the system then the angular momentum of that system remains constant". If an object is tied to a string and whirled in a circular path with uniform speed, the angular momentum of the system will still remain conserved even after the string is cut as no any external torque is applied on that system.

 
 
 

113. A wheel moving down a perfectly frictionless inclined plane will undergo slipping instead of rolling. Why?

A body rolls due to force of friction acting on it. If the wheel is moving down a perfectly frictionless inclined plane, it will be under the effect of its weight only. Since, weight of the wheel acts along vertical through its center of mass, the wheel will not rotated but will keep on slipping. Hence, a wheel moving down a perfectly frictionless inclined plane will undergo slipping instead of rolling.

 
 
 

114. A circular platform is rotating with a uniform angular velocity. What will be the change in the motion of the platform if a person sits person sits near the edge and then stars moving towards the center of the platform?

Every system will try to keep the angular momentum L conserved in absence of external torque (where I is moment of inertia & w be the angular velocity). When the person sits near the edge of the platform, the value of moment of inertia i.e. I will be increased. For the angular momentum L to remain conserved, its  angular velocity w has to be decreased and the platform will slow down. When the person starts moving towards the center of the platform, moment of inertia (I) will decrease while its angular velocity w will increase and the platform motion will be fast.

 
 
 

115. Why is ladder more likely to slip when a person is high upon it than when he just begins to climb?

When a person is high up, the moment of force tending to rotate the ladder increases because of greater lever arm. When he just begins to climb, the lever arm will be decreased and the moment of force will be insufficient to cause slipping. Hence, ladder is more likely to slip when a person is high upon it than when he just begins to climb.

 

116. Some toys are made with their bases filled with clay or lead shots. Why?

As the body will be stable if its center of gravity i.e. C.G. lies within the base of the body. When the base of some toys are made heavy, there is a shifting of center of gravity to the base of toys so that they are stable i.e. it causes the toys to remain in stable equilibrium. Hence, some toys are made with their bases filled with clay or lead shots. 

 

117. A rope dancer holds an umbrella or pole to balance him. Why?

As the body will be stable if its center of gravity i.e. C.G. lies within the base of the body. A ropedancer holds an umbrella or pole to balance him in order to shift the center of gravity i.e. C.G. within the base so that he or she can enjoy stable equilibrium by gaining stability. Hence, a ropedancer holds an umbrella or pole to balance him.

 

118. A man carrying a load on his back leans forward. Why? (HSEB 1996).

As the body will be stable if its center of gravity i.e. C.G. lies within the base of the body. A man carrying a load on his back leans forward so that the vertical line through C.G. passes through the base. Further, the position of C.G. will be lowered with respect to the ground and makes him in stable equilibrium. Hence, a man carrying a load on his back leans forward.

 

119. While coming down the hill, a person leans backwards. Why?

As the body will be stable if its center of gravity i.e. C.G. lies within the base of the body. While coming down the hill, a person leans backwards so that the vertical line through the center of gravity i.e. C.G. lies within the base. Further the height of C.G. will be decreased and he enjoys stable equilibrium state. Hence, a person leans backwards while coming down the hill in order to gain stability.

 

120. Trucks, cars and ships are made with their base heavy. Why? (HSEB 1994)

As the body will be stable if its center of gravity i.e. C.G. lies within the base of the body i.e. the base of that body is to be made heavy in order to make that body stable. The base of trucks, cars & ships are made heavy in order to shift the position of center of mass C.M. within the base of vehicles or ship in order that they will enjoy stable equilibrium. Hence, trucks, cars and ships are made with their base heavy.

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