MEDIUM
JEE Advanced
IMPORTANT
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A car must be parked in a small gap between the cars parked in a row along the pavement. Should the car be driven out forwards or backwards for the manoeuvre if only its front wheels can be turned?

Important Questions on Mechanics

HARD
JEE Advanced
IMPORTANT

An aeroplane flying along the horizontal at a velocity v0 starts to ascend, describing a circle in the vertical plane. The velocity of the plane changes with height $h$ above the initial level of motion according to the law v2=v02-2a0h. The velocity of the plane at the upper point of the trajectory is v1=v02.

Determine the acceleration a of the plane at the moment when its velocity is directed vertically upwards.

MEDIUM
JEE Advanced
IMPORTANT

An open merry-go-round rotates at an angular velocity ω. A person stands in it at a distance r from the rotational axis. It is raining, and the raindrops fall vertically at a velocity v0.

How should the person hold an umbrella to protect himself from the rain in the best way?

HARD
JEE Advanced
IMPORTANT

A bobbin rolls without slipping over a horizontal surface so that the velocity v of the end of the thread (point A) is directed along the horizontal. A board hinged at point B leans against the bobbin (Fig.). The inner and outer radii of the bobbin are r and R respectively.

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Determine the angular velocity ω of the board as a function of an angle α.

HARD
JEE Advanced
IMPORTANT

A magnetic tape is wound on an empty spool rotating at a constant angular velocity. The final radius r2 of the winding was found to be three times as large as the initial radius r1 (Figure). The winding time of the tape is t1.

What is the time t2 required for winding a tape whose thickness is half that of the initial tape?

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HARD
JEE Advanced
IMPORTANT
It was found that the winding radius of a tape on a cassette was reduced by half in a time t1=20 min of operation. In what time t2 will the winding radius be reduced by half again?
HARD
JEE Advanced
IMPORTANT

Two rings O and O'are put on two vertical stationary rods AB and A'B' respectively. An inextensible thread is fixed at point A' and on ring O and is passed through ring O' (Fig.).

Assuming that ring O' moves downwards at a constant velocity v1, determine the velocity v2 of ring O if AOO'=α

Question Image.

MEDIUM
JEE Advanced
IMPORTANT

A weightless inextensible rope rests on a stationary wedge forming an angle α with the horizontal (Fig.). One end of the rope is fixed to the wall at point A. A small load is attached to the rope at point B. The wedge starts moving to the right with a constant acceleration a.

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Determine the acceleration a1 of the load when it is still on the wedge.

MEDIUM
JEE Advanced
IMPORTANT
An ant runs from an ant-hill in a straight line so that its velocity is inversely proportional to the distance from the centre of the ant-hill. When the ant is at point A at a distance l1=1 m from the centre of the ant-hill, its velocity v1=2 cm s-1.
What time will it take the ant to run from point A to point B which is at a distance l2=2 m from the centre of the anthill?