A student skates up a ramp that makes an angle 30$$^\circ$$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v0 and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)
A
$$v_0^2 - 2gh = {1 \over 2}gR$$
B
$$v_0^2 - 2gh = {{\sqrt 3 } \over 2}gR$$
C
the centripetal force required at points x and z is zero
D
the centripetal force required is maximum at points x and z
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure.
When the distance of the piston from closed end is L = L0, the particle speed is v = v0. The piston is moved inward at a very low speed V such that $$V < < {{dL} \over L}{v_0}$$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
A
After each collision with the piston, the particle speed increases by 2V.
B
If the piston moved inward by dL, the particle speed increases $$2v{{dL} \over L}$$.
C
The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to 1/2 L0.
D
The rate at which the particle strikes the piston is v/L.
3
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A particle of mass $$m$$ is initially at rest at the origin. It is subjected to a force and starts moving along the $$x$$-axis. Its kinetic energy $$K$$ changes with time as $$dK/dt = \gamma t,$$ where $$\gamma $$ is a positive constant of appropriate dimensions. Which of a positive constant of appropriate dimensions. Which of the following statement is (are) true?
A
The force applied on the particle is constant
B
The speed of the particle is proportional to time
C
The distance of the particle from the origin increases linearly with time
D
The force is conservative
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A flat plate is moving normal to its plane through a gas under the reaction of a constant force $$F.$$ The gas is kept at a very low pressure. The speed of the plate $$v$$ is much less than the average speed u of the gas molecules.
Which of the following options is /are true?
A
The pressure difference between the leading and trailing faces of the plate is proportional to uv
B
The resistive force experimenced by the plate is proportional to $$v$$
C
The plate will continue to move with constant non-zero acceleration, at all times
D
At a later time the external force $$F$$ balances the resistive force
