1
GATE ME 2016 Set 1
Numerical
+2
-0
A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is $$0.25.$$ The string can withstand a maximum force of $$20$$ N. The maximum value of the mass (m) for which the string will not break and the block will be in static equilibrium is ____________ kg.
Take $$\cos \theta = 0.8$$ and $$\sin \theta = 0.6$$. Acceleration due to gravity g $$=$$ $$10$$ m/s2
2
GATE ME 2016 Set 1
+2
-0.6
A two-member truss $$PQR$$ is supporting a load W. The axial forces in members $$PQ$$ and $$QR$$ are respectively
A
$$2W$$ tensile and $$\sqrt 3 W$$ compressive
B
$$\sqrt 3 W$$ tensile and $$2W$$ compressive
C
$$\sqrt 3 W$$ compressive and $$2W$$ tensile
D
$$2W$$ compressive and $$\sqrt 3 W$$ tensile
3
GATE ME 2016 Set 2
+2
-0.6
A system of particles in motion has mass center $$G$$ as shown in the figure. The particle $$i$$ has mass $${m_i}$$ and its position with respect to a fixed point $$O$$ is given by the position vector $${r_i}$$ . The position of the particle with respect to $$G$$ is given by the vector $${\rho _i}$$ . The time rate of change of the angular momentum of the system of particles about $$G$$ is (The quantity $$\mathop {{\rho _i}}\limits^{..}$$ indicates second derivative of $${\rho _i}$$ with respect to time and likewise for $${r _i}$$).
A
$$\,\,{\sum {_i{r_i} \times {m_i}\mathop \rho \limits^{..} } _i}$$
B
$${\sum {_i{\rho _i} \times {m_i}\mathop r\limits^{..} } _i}$$
C
$${\sum {_i{r_i} \times {m_i}\mathop r\limits^{..} } _i}$$
D
$${\sum {_i{\rho _i} \times {m_i}\mathop \rho \limits^{..} } _i}$$
4
GATE ME 2016 Set 3
Numerical
+2
-0
A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed v of the disc when it reaches position B is _________ m/s.
Acceleration due to gravity g = 10 m/s2