1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is :
A
$$2\sqrt {{k \over p}} $$
B
$$2\sqrt {{p \over k}} $$
C
$$\sqrt {{{2p} \over 2}} $$
D
$$\sqrt {{{2k} \over p}} $$

Explanation

$${{dp} \over {dt}} = F = kt$$

$$\int_P^{3P} {dP} = \int_0^T {kt\,dt} $$

$$2p = {{K{T^2}} \over 2}$$

$$T = 2\sqrt {{P \over K}} $$
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 12th January Morning Slot

The position vector of the centre of mass $$\overrightarrow r {\,_{cm}}\,$$ of an asymmetric uniform bar of negligible area of crosssection as shown in figure is :

A
$${\overrightarrow r _{cm}}\, = {{11} \over 8}L\,\,\widehat x + {8 \over 8}L\widehat y$$
B
$${\overrightarrow r _{cm}}\, = {5 \over 8}L\,\,\widehat x + {{13} \over 8}L\widehat y$$
C
$${\overrightarrow r _{cm}}\, = {{13} \over 8}L\,\,\widehat x + {5 \over 8}L\widehat y$$
D
$${\overrightarrow r _{cm}}\, = {3 \over 8}L\,\,\widehat x + {{11} \over 8}L\widehat y$$

Explanation



$${X_{cm}} = {{2mL + 2mL + {{5mL} \over 2}} \over {4m}} = {{13} \over 8}L$$

$${Y_{cm}} = {{2m \times L + m \times \left( {{L \over 2}} \right) + m \times 0} \over {4m}} = {{5L} \over 8}$$
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 12th January Morning Slot

A simple pendulum, made of a string of length $$\ell $$ and a bob of mass m, is released from a small angle $${{\theta _0}}$$. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $${{\theta _1}}$$. Then M is given by :
A
$${m \over 2}\left( {{{{\theta _0} + {\theta _1}} \over {{\theta _0} - {\theta _1}}}} \right)$$
B
$${m \over 2}\left( {{{{\theta _0} - {\theta _1}} \over {{\theta _0} + {\theta _1}}}} \right)$$
C
$$m\left( {{{{\theta _0} + {\theta _1}} \over {{\theta _0} - {\theta _1}}}} \right)$$
D
$$m\left( {{{{\theta _0} - {\theta _1}} \over {{\theta _0} + {\theta _1}}}} \right)$$

Explanation



v = $$\sqrt {2g\ell \left( {1 - \cos {\theta _0}} \right)} $$

v1 = $$\sqrt {2g\ell \left( {1 - \cos {\theta _1}} \right)} $$

By momentum conservation

m$$\sqrt {2gl\left( {1 - \cos {\theta _0}} \right)} $$
$$= M{V_m} - m\sqrt {2g\left( {1 - \cos \theta } \right)} $$

$$ \Rightarrow $$$$m\sqrt {2g\ell } \left\{ {\sqrt {1 - \cos {\theta _0}} + \sqrt {1 - \cos {\theta _1}} } \right\}$$

$$ = $$ MVm

and  e = 1 = $${{{V_m} + \sqrt {2g\ell \left( {1 - \cos {\theta _1}} \right)} } \over {\sqrt {2g\ell \left( {1 - \cos {\theta _0}} \right)} }}$$

$$\sqrt {2g\ell } $$ $$\left( {\sqrt {1 - \cos {\theta _0}} - \sqrt {1 - \cos {\theta _1}} } \right) $$
$$= $$ Vm     . . .(I)

m$$\sqrt {2g\ell } \left( {\sqrt {1 - \cos {\theta _0}} + \sqrt {1 - \cos {\theta _1}} } \right)$$
$$ = $$ MVM     . . .(II)

Dividing

$${{\left( {\sqrt {1 - \cos {\theta _0}} + \sqrt {1 - \cos {\theta _1}} } \right)} \over {\left( {\sqrt {1 - \cos {\theta _0}} + \sqrt {1 - \cos {\theta _1}} } \right)}} = {M \over m}$$

By componendo divided

$${{m - M} \over {m + M}}$$ = $${{\sqrt {1 - \cos {\theta _1}} } \over {\sqrt {1 - \cos {\theta _0}} }} = {{\sin \left( {{{{\theta _1}} \over 2}} \right)} \over {\sin \left( {{{{\theta _0}} \over 2}} \right)}}$$

$$ \Rightarrow $$  $${M \over m} = {{{\theta _0} - {\theta _1}} \over {{\theta _0} + {\theta _1}}} \Rightarrow M = {{{\theta _0} - \theta 1} \over {{\theta _0} + {\theta _1}}}$$
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 8th April Morning Slot

If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s, the pressure exerted by the gas molecules will be of the order of :
A
108 N/m2
B
1016 N/m2
C
104 N/m2
D
2 N/m2

Questions Asked from Impulse & Momentum

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Name Indicates No of Questions
AIEEE 2004 (1)
keyboard_arrow_right
AIEEE 2005 (1)
keyboard_arrow_right
AIEEE 2006 (1)
keyboard_arrow_right
AIEEE 2010 (2)
keyboard_arrow_right
JEE Main 2013 (Offline) (1)
keyboard_arrow_right
JEE Main 2015 (Offline) (1)
keyboard_arrow_right
JEE Main 2018 (Online) 15th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 11th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th January Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 8th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Morning Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 9th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Morning Slot (3)
keyboard_arrow_right
JEE Main 2019 (Online) 10th April Evening Slot (2)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Morning Slot (1)
keyboard_arrow_right
JEE Main 2019 (Online) 12th April Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 9th January Evening Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 3rd September Morning Slot (1)
keyboard_arrow_right
JEE Main 2020 (Online) 6th September Evening Slot (1)
keyboard_arrow_right
JEE Main 2021 (Online) 26th February Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 16th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 17th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 18th March Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 20th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 22th July Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 25th July Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th July Morning Shift (2)
keyboard_arrow_right
JEE Main 2021 (Online) 26th August Evening Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 27th August Morning Shift (1)
keyboard_arrow_right
JEE Main 2021 (Online) 31st August Morning Shift (2)
keyboard_arrow_right

EXAM MAP

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE ME GATE PI GATE EE GATE CE GATE IN

Medical

NEET