1
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ is along the ground and $${\widehat j}$$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:
A
y = x - 5x2
B
y = 2x - 5x2
C
4y = 2x - 5x2
D
4y = 2x - 25x2
2
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
This question has statement $${\rm I}$$ and statement $${\rm I}$$$${\rm I}$$. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement - $${\rm I}$$: A point particle of mass $$m$$ moving with speed $$\upsilon $$ collides with stationary point particle of mass $$M.$$ If the maximum energy loss possible is given as $$f\left( {{1 \over 2}m{v^2}} \right)$$, then $$f = \left( {{m \over {M + m}}} \right).$$

Statement - $${\rm II}$$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A
Statement - $${\rm I}$$ is true, Statement - $${\rm II}$$ is true; Statement - $${\rm II}$$ is the correct explanation of Statement - $${\rm I}$$.
B
Statement - $${\rm I}$$ is true, Statement - $${\rm II}$$ is true; Statement - $${\rm II}$$ is not the correct explanation of Statement - $${\rm I}$$.
C
Statement - $${\rm I}$$ is true, Statement - $${\rm II}$$ is false
D
Statement - $${\rm I}$$ is false, Statement - $${\rm II}$$ true.
3
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it cases to slip?
A
$${{r{\omega _0}} \over 4}$$
B
$${{r{\omega _0}} \over 3}$$
C
$${{r{\omega _0}} \over 2}$$
D
$${r{\omega _0}}$$
4
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?
A
$${{5GmM} \over {6R}}$$
B
$${{2GmM} \over {3R}}$$
C
$${{GmM} \over {2R}}$$
D
$${{GmM} \over {3R}}$$
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