1
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
$${\sum {_i{\rho _i} \times {m_i}\mathop \rho \limits^{..} } _i}$$
2
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
3
GATE ME 2016 Set 3
Numerical
+2
-0
An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is __________ .
4
GATE ME 2016 Set 3
Numerical
+2
-0
A rigid rod $$(AB)$$ of length $$L = \sqrt 2$$ m is undergoing translational as well as rotational motion in the $$x-y$$ plane (see the figure). The point $$A$$ has the velocity $${V_1} = \widehat i + 2\widehat jm/s.$$ The end $$B$$ is constrained to move only along the $x$$direction. The magnitude of the velocity$${V_2}$$(in$$m/s$$) at the end$$B$ is __________