HARD
JEE Main
IMPORTANT
Earn 100

A particle is moving along the -axis with its coordinate with time given by Another particle is moving along the -axis with its coordinate as a function of time given by At the speed of the second particle as measured in the frame of the first particle is given as Then is ___________.

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Important Questions on Laws of Motion
MEDIUM
JEE Main
IMPORTANT
A block of mass is kept on a rough inclined plane as shown in the figure. A force of is applied on the block. The coefficient of static friction between the plane and the block is What should be the minimum value of force such that the block does not move downward? (take )


MEDIUM
JEE Main
IMPORTANT
A mass of is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is

HARD
JEE Main
IMPORTANT
A ball is thrown upward with an initial velocity from the surface of the earth. The motion of the ball is affected by a drag force equal to (where is mass of the ball, is its instantaneous velocity and is a constant). Time taken by the ball to rise to its zenith is:

MEDIUM
JEE Main
IMPORTANT
Two blocks and of masses and are kept on the table as shown in figure. The coefficients of friction between and is and between and the surface of the table is also The maximum force that can be applied on horizontally, so that the block does not slide over the block is : [Take ]


HARD
JEE Main
IMPORTANT
A man (mass ) and his son (mass ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of with respect to the man. The speed of the man with respect to the surface is:

HARD
JEE Main
IMPORTANT
A smooth wire of length is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed about the vertical diameter as shown in figure, the bead is at rest with respect to the circular ring at position as shown. Then the value of is equal to:


HARD
JEE Main
IMPORTANT
A block of mass is (i) pushed in case and (ii) pulled in case by a force making an angle of with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is The difference between the accelerations of the block, in case and case will be:

EASY
JEE Main
IMPORTANT
A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force down the inclined plane. The maximum external force up the inclined plane that does not move the block is The coefficient of static friction between the block and the plane is: [Take ]

