JEE Main 2020 (Online) 5th September Evening Slot | Laws of Motion Question 100 | Physics

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv²(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

-bv³(t)

$$ - {{2b{v^3}} \over {M\left( t \right)}}$$

$$ - {{b{v^3}} \over {M\left( t \right)}}$$

$$ - {{b{v^3}} \over {2M\left( t \right)}}$$

JEE Main 2020 (Online) 4th September Evening Slot

MCQ (Single Correct Answer)

-1

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv² where v is its speed. The maximum height attained by the ball is :

$${1 \over k}{\tan ^{ - 1}}{{k{u^2}} \over {2g}}$$

$${1 \over {2k}}{\tan ^{ - 1}}{{k{u^2}} \over g}$$

$${1 \over {2k}}\ln \left( {1 + {{k{u^2}} \over g}} \right)$$

$${1 \over k}\ln \left( {1 + {{k{u^2}} \over {2g}}} \right)$$

JEE Main 2020 (Online) 7th January Evening Slot

MCQ (Single Correct Answer)

-1

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45^o with the vertical. Then F equal : (Take g = 10 ms^–2 and the rope to be massless)

100 N

75 N

90 N

70 N

JEE Main 2019 (Online) 12th April Evening Slot

MCQ (Single Correct Answer)

-1

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l₁ and l₂ where, l₁ = nl₂ and n is an integer. The ratio k₁/k₂ of the corresponding force constant, k₁ and k₂ will be :

$${1 \over {{n^2}}}$$

$${1 \over n}$$

n²

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