Motion in a Lane MCQs for NEET — Physics Questions with Answers

$ \triangle S = \sqrt { R^2 + R^2 - 2R^2 cos \theta } $ $ \triangle S= \sqrt { 2R^2 - 2R^2 Cos \theta } = \sqrt { 2R^2 (1 - Cos \theta ) }$ $ = 2 R sin { \theta \over 2 } $

To find the time to reach the maximum height, we use the kinematic equation for a projectile. The time to reach the maximum height (tm) is given by: \[ t_m = rac{u ext{sin} heta}{g} \\] The maximum height (H) is given by: \[ H = rac{u^2 ext{sin}^2 heta}{2g} \\] Rearranging to solve for tm, we get: \[ t_m = rac{u ext{sin} heta}{g} = rac{ ext{sin} heta}{g} imes rac{u^2 ext{sin} heta}{2u} \\] \[ t_m = rac{2H}{g} imes rac{1}{u} \\] Simplifying, we get: \[ t_m = rac{2H}{g} = rac{2H}{g} \\] Therefore, the correct option is o2: \[ t_m = rac{ ext{2H}}{g} \\]

The equations given for displacement are x = 3sin(2t) and y = 3cos(2t). These represent parametric equations of a circle with radius 3. The speed of a particle moving in a circle with constant radius and angular speed is constant. Thus, the speed is constant and non-zero. Hence, option o2 is correct.

A vector quantity is defined by having both a magnitude and a direction. For example, velocity is a vector because it specifies how fast something is moving (magnitude) and in which direction. Therefore, to introduce a vector quantity, it needs both magnitude and direction.

Electric current is a scalar quantity. Unlike vectors, scalar quantities have only magnitude and no direction. Electric current is described by its magnitude, which is the rate of flow of charge through a conductor, but it does not have a specific direction in the sense that a vector does.

If two vectors $ \\vec{P} and \\vec{Q} $ are equal, it means they have both the same magnitude and the same direction. Therefore, $ \\vec{P} and \\vec{Q} $ are parallel to each other.

For two vectors \( \vec{P} \) and \( \vec{Q} \) to be equal, they must have both equal magnitudes and the same direction. This is because vectors are defined by both their magnitude and direction. Therefore, \( \vec{P} = \vec{Q} \) is true if and only if their magnitudes are equal and they are in the same direction.

When two vectors \( \vec{A} \) and \( \vec{B} \) are in opposite directions, they are referred to as antiparallel vectors. Antiparallel vectors have the same magnitude but opposite directions. This is different from parallel vectors, which have the same direction.

$$ \vec C = \vec A + \vec B $$ $$ C^2 = A^2 + B^2 + 2AB cos \theta $$

The resultant of two forces can be found using the triangle law of vector addition. The magnitude of the resultant force \( \vec{R} \) of two forces of magnitudes 2N and 3N can range from the absolute difference of the two forces to the sum of the two forces. Hence, \( |2N - 3N| \leq R \leq 2N + 3N \), which simplifies to \( 1N \leq R \leq 5N \). Therefore, a resultant force of 0.5N is not possible.