GATE ME 2003 | GATE ME Year Wise Previous Years Questions

GATE ME 2003

MCQ (Single Correct Answer)

-0.3

The solution of the differential equation $${{dy} \over {dx}} + {y^2} = 0$$ is

$$y = {1 \over {x + c}}$$

$$y = - {{{x^3}} \over 3} + c$$

$$c\,\,{e^x}$$

unsolvable as equation is non-linear

GATE ME 2003

MCQ (Single Correct Answer)

-0.6

A reel of mass $$'‘m'’$$ and radius of gyration $$'‘'k’$$ is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. Consider the thickness of the thread and its mass negligible in comparison with radius $$‘'r'’$$ of the hub and the reel mass $$‘'m'’$$, Symbol $$'‘g’'$$ represents the acceleration due to gravity. GATE ME 2003 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 60 English

GATE ME 2003 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 60 English

The tension in thread is

$${{mg{r^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$

$${{mg{k^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$

$${{mgrk} \over {\left( {{r^2} + {k^2}} \right)}}$$

$${{mg} \over {\left( {{r^2} + {k^2}} \right)}}$$

GATE ME 2003

MCQ (Single Correct Answer)

-0.6

GATE ME 2003 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 61 English

The linear acceletation of the reel is:

$${{g{r^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$

$${{g{k^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$

$${{grk} \over {\left( {{r^2} + {k^2}} \right)}}$$

$${{mg{r^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$

GATE ME 2003

MCQ (Single Correct Answer)

-0.3

A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass ‘M’ initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance ‘s’ along the floor. Assuming $$\mu $$ to be the coefficient to kinetic friction between the block and the floor and ‘g’ the acceleration due to gravity what is the velocity v of the bullet? GATE ME 2003 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 89 English

GATE ME 2003 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 89 English

$${{M + m} \over m}\sqrt {2\mu gS} $$

$${{M - m} \over m}\sqrt {2\mu gS} $$

$${{\mu \left( {M + m} \right)} \over m}\sqrt {2gS} $$

$${M \over m}\sqrt {2\mu gS} $$

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