1
GATE ME 2004
+2
-0.6
The figure below shown a pair of pin jointed gripper tongs holding an object weighing $$2000N$$. The coefficient of friction (µ) at the gripping surface is $$0.1$$ $$XX$$ is the line of action of the input force and $$Y - Y$$ is the line of application of gripping force. If the pin joint is assumed to be frictionless, the magnitude of force $$F$$ required to hold the weight is
A
$$1000$$ $$N$$
B
$$2000$$ $$N$$
C
$$2500$$ $$N$$
D
$$5000$$ $$N$$
2
GATE ME 2004
+2
-0.6
A rigid body shown in the fig.(a) has a mass of 10kg. It rotates with a uniform angular velocity $$'\omega '$$ A balancing mass of 20 kg is attached as shown in fig.(b). The percentage increase in mass moment of inertia as a result of this addition is
A
25%
B
50%
C
100%
D
200%
3
GATE ME 2004
+2
-0.6
An ejector mechanism consists of a helical compression spring having a spring constant of k = 981 × 103 N/m. It is pre-compressed by 100mm from its free state. If it is used to eject mass of 100kg heald on it, the mass will move up through a distance of
A
$$100$$ $$mm$$
B
$$5000$$ $$mm$$
C
$$581$$ $$mm$$
D
$$1000$$ $$mm$$
4
GATE ME 2003
+2
-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.

The linear acceletation of the reel is:

A
$${{g{r^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$
B
$${{g{k^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$
C
$${{grk} \over {\left( {{r^2} + {k^2}} \right)}}$$
D
$${{mg{r^2}} \over {\left( {{r^2} + {k^2}} \right)}}$$
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