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Published on: 31/05/2021
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1.
It was summer season and Ishant was sleeping at top of roof when heard some noise at downstairs when he looked down, he saw that two robbers were holding his brother at gun point , suddenly he saw a big drum near to him and he rolled the drum from the stairs which hit one of the robber who was holding gun and robber fell down. In mean time other one run away and the family caught that robber and handed him over to the police.
What is meant by rolling without slipping?
2.
It was summer season and Ishant was sleeping at top of roof when heard some noise at downstairs when he looked down, he saw that two robbers were holding his brother at gun point, suddenly he saw a big drum near to him and he rolled the drum from the stairs which hit one of the robber who was holding gun and robber fell down. In mean time other one run away and the family caught that robber and handed him over to the police.
If a thin hollow cylinder, opened at both the ends and weighing 5 kg rolls with a speed of 10 m/s without slipping. What is the kinetic energy of cylinder?
3.
It was summer season and Ishant was sleeping at top of roof when heard some noise at downstairs when he looked down, he saw that two robbers were holding his brother at gun point, suddenly he saw a big drum near to him and he rolled the drum from the stairs which hit one of the robber who was holding gun and robber fell down. In mean time other one run away and the family caught that robber and handed him over to the police.
What kind of motion is described by the drum?
4.
It was summer season and Ishant was sleeping at top of roof when heard some noise at downstairs when he looked down, he saw that two robbers were holding his brother at gun point, suddenly he saw a big drum near to him and he rolled the drum from the stairs which hit one of the robber who was holding gun and robber fell down. In mean time other one run away and the family caught that robber and handed him over to the police.
(i) What values of Ishant saved his brother's life?
(ii) What kind of motion is described by the drum?
(iii) If a thin hollow cylinder, opened at both the ends and weighing 5 kg rolls with a speed of 10 m/s without slipping. What is the kinetic energy of cylinder?
(iv) What is meant by rolling without slipping?
1.
If an object rolls across a surface in such a way that there is no relative motion of object and surface at point of contact, then the motion is called rolling without slipping.
2.
Given, m = 5 kg, v = 10 m/s
As cylinder rolls without slipping so it has translational and rotational KE.
\(\therefore KE=\frac { 1 }{ 2 } { mv }^{ 2 }+\frac { 1 }{ 2 } { I\omega }^{ 2 }\)
\(As\quad I=m{ r }^{ 2 }\quad and\quad v=r\omega \)
\(So,\quad KE=\frac { 1 }{ 2 } { mv }^{ 2 }+\frac { 1 }{ 2 } { (m{ r }^{ 2 })\omega }^{ 2 }\)
\(=\frac { 1 }{ 2 } { mv }^{ 2 }+\frac { 1 }{ 2 } { mv }^{ 2 }\)
\(={ mv }^{ 2 }=5\times { 10 }^{ 2 }=500J\).
3.
Rolling motion, i.e. (Rotation + Translation)
4.
(i) Mental alertness, bravery, presence of mind and quick decision.
(ii) Rolling motion, i.e. (Rotation + Translation)
(iii) Given, m = 5 kg, v = 10 m/s
As cylinder rolls without slipping so it has translational and rotational KE.
\(\therefore KE=\frac { 1 }{ 2 } { mv }^{ 2 }+\frac { 1 }{ 2 } { I\omega }^{ 2 }\)
\(As\quad I=m{ r }^{ 2 }\quad and\quad v=r\omega \)
\(So,\quad KE=\frac { 1 }{ 2 } { mv }^{ 2 }+\frac { 1 }{ 2 } { (m{ r }^{ 2 })\omega }^{ 2 }\)
\(=\frac { 1 }{ 2 } { mv }^{ 2 }+\frac { 1 }{ 2 } { mv }^{ 2 }\)
\(={ mv }^{ 2 }=5\times { 10 }^{ 2 }=500J\).
(iv) If an object rolls across a surface in such a way that there is no relative motion of object and surface at point of contact, then the motion is called rolling without slipping.
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