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A particle moves in the X–Y plane under the influence of a force such that its linear momentum is $ \vec P (t) = A[ \hat i cos (kt) -\hat j sin(kt)] $ where A and k are constants .The angle betweenn the force and momentum is

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Explanation

$ \vec P (t) = A[ \hat i cos (kt) -\hat j sin(kt)] $ $ \vec F = { d \over dt} \left ( \vec P (t) \right) $ $ = Ak \left( - \hat i sin kt - \hat j cos ky \right) $ $ \vec F . \vec P = A^2 k ( -cos kt .sin kt + sin kt . cos kt ) $ $ \vec F . \vec P = 0 $

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Force of 5 N acts on a body of weight 9.8 N. what is the acceleration produced in $ms^{-2}$

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Explanation

As weight W = mg = 9.8 N Therefore m = 1 Kg a = F / m

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Same force acts on two bodies of different masses 2 kg and 4 kg initially at rest. The ratio of times required to acquire same final velocity is

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Explanation

$ t = {V \over a } \Rightarrow t \alpha { 1 \over a } ( v is constant ) $ $ \therefore {t_1 \over t_2 } = {a_2 \over a_1} = { m_1 \over m_2 } = {2 \over 4 } = { 1 \over 2 } $ $ a \alpha 1/m as F is constant $

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Which of the following quantities measured from different inertial reference frames are same

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Explanation

Force is a quantity that is invariant under Galilean transformations between different inertial reference frames. This means that when observed from different inertial frames, the force remains the same. In contrast, quantities like velocity, displacement, and kinetic energy can vary depending on the reference frame.

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When the speed of a moving body is doubled

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A particle moves in the XY Plane under the action of a force F such that the components of its linear momentum P at any time t are Px = 2 cost, Py = 2 sint. The angle between F and P at time t is

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Explanation

$ \vec P = Px \hat i + Py \hat j , \vec F = { \vec {dp} \over dt} $ Now $ \vec F . \vec P = 0 $ $ \therefore \theta = 90 ^\circ $

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A player caught a cricket ball of mass 150 g moving at the rate of $20 ms^{-1} $ . If the catching process be completed in 0.1 s the force of the blow exerted by the ball on the hands of player is

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Explanation

Force exerted by ball, F = m (dv /dt)

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A body of mass 5 kg starts from the origin with an initial velocity $ \vec u = 30 \hat i + 40 \hat j ms^{-1} $. If a constant Force
$ \vec F = - \left( \hat i + 5 \hat j \right) N $ acts on the body, the time in which the y-component of the velocity becomes

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Explanation

$ \nu_y = 40ms^{-1} Fy = -5N m = 5kg $ $ so a_y = { F_y \over m } = -1 ms^{-1} $ $ as V_y = u_y + at $ $ 0 = 40 -lt \Rightarrow t = 40 s $

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A cold soft drink is kept on the balance.When the cap is open, then the weight

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Explanation

Gas will cane out with sufficient speed in forward direction, So recetion of this forward force wil change the reading of the spring balance.

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A wagon weighing 1000 kg is moving with a velocity $50 km h^{-1}$ on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is

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Explanation

According to the principle of conservation of linear momentum $ 1000 \times 50 = {1250 \times \nu \over \nu} = 40 km/h $

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