Physics Mechanics Quiz

The dimensional formula for 'a' is $M L^5 T^{-2}$.

Average velocity is the ratio of total displacement to total time, while average speed is the ratio of total path length to total time.

Instantaneous velocity is the velocity of an object at a specific instant in time, reflecting its speed at that moment.

<p>Uniform motion occurs when an object covers equal distances in equal time intervals.</p> Signup and view all the answers

<p>The principle of homogeneity states that quantities in an equation must have the same dimensions to be added or subtracted.</p> Signup and view all the answers

<p>Average speed is calculated by dividing the total path length by the total time interval.</p> Signup and view all the answers

<p>'a' corrects for intermolecular forces, while 'b' accounts for the volume occupied by gas molecules.</p> Signup and view all the answers

<p>3.6 N s</p> Signup and view all the answers

<p>For every action, there is an equal and opposite reaction.</p> Signup and view all the answers

<p>They act on different bodies, so they do not cancel each other despite being equal and opposite.</p> Signup and view all the answers

<p>The scale would read 70 kg.</p> Signup and view all the answers

<p>The scale would read zero.</p> Signup and view all the answers

<p>The formula is $T = \frac{2u \sin \theta}{g}$.</p> Signup and view all the answers

<p>The horizontal range is calculated as $R = u \cos \theta \times T$ where $T$ is the time of flight.</p> Signup and view all the answers

<p>The range R is maximized when the launch angle is $\theta = 45^\circ$.</p> Signup and view all the answers

<p>For angles $\theta$ and $(90 - \theta)$, $R = \frac{u^2 \sin 2\theta}{g}$ and $R = \frac{u^2 \sin (180 - 2\theta)}{g}$ yield the same result since $\sin(180 - 2\theta) = \sin 2\theta$.</p> Signup and view all the answers

<p>The maximum height H is defined as the peak vertical distance attained by the projectile during its flight.</p> Signup and view all the answers

<p>Gravity acts as a downward acceleration that influences the vertical motion of the projectile, affecting both time of flight and maximum height.</p> Signup and view all the answers

<p>Increasing the initial launch speed u directly increases the time of flight T, as seen in the formula $T = \frac{2u \sin \theta}{g}$.</p> Signup and view all the answers

<p>The angle affects the trade-off between horizontal range and maximum height, with angles around $45^\circ$ optimizing both.</p> Signup and view all the answers

<p>The commutative property of vector addition.</p> Signup and view all the answers

<p>A - B can be defined as A + (-B).</p> Signup and view all the answers

<p>It states that the resultant of two vectors is represented by the diagonal of a parallelogram formed by the vectors.</p> Signup and view all the answers

<p>A unit vector is a vector of unit magnitude that specifies direction, often represented as Ā = |𝐴̅|𝐴̂.</p> Signup and view all the answers

<p>The unit vectors are denoted by î, ĵ, and k̂ respectively.</p> Signup and view all the answers

<p>Vector A can be resolved into components along the unit vectors î and ĵ.</p> Signup and view all the answers

<p>The magnitude is given by R = √(A² + B² + 2AB cos θ).</p> Signup and view all the answers

<p>Unit vectors must satisfy |î| = |ĵ| = |k̂| = 1.</p> Signup and view all the answers

<p>It represents the relationship between angular momentum (𝑙), the position vector (𝑟), and linear momentum (𝑝).</p> Signup and view all the answers

<p>Differentiating provides the rate of change of angular momentum with respect to time, which relates to torque.</p> Signup and view all the answers

<p>Torque affects the rate of change of angular momentum, as shown by the relation d𝑙/d𝑡 = 𝜏.</p> Signup and view all the answers

<p>Torque can be expressed as τ = r × F, where r is the position vector and F is the applied force.</p> Signup and view all the answers

<p>It indicates that linear momentum (p) is the product of mass (m) and velocity (v) of a particle.</p> Signup and view all the answers

<p>Angular momentum remains constant if no external torque is acting on the system.</p> Signup and view all the answers

<p>It represents the angular momentum due to linear momentum at a specific position vector.</p> Signup and view all the answers

<p>It indicates that in the absence of torque, the angular momentum does not change over time.</p> Signup and view all the answers

<p>Torque is the rate of change of angular momentum, expressed as $\vec{\tau} = \frac{d\vec{L}}{dt}$.</p> Signup and view all the answers

<p>If the total external torque on a system of particles is zero, then the total angular momentum remains constant.</p> Signup and view all the answers

<p>Torque can be calculated using the cross product: $\vec{\tau} = \vec{r} \times \vec{F}$.</p> Signup and view all the answers

<p>A rigid body is in mechanical equilibrium if both the total external force and total external torque acting on it are zero.</p> Signup and view all the answers

<p>Translational equilibrium occurs when the total external force on a rigid body is zero, indicating no change in linear momentum.</p> Signup and view all the answers

<p>Rotational equilibrium is achieved when the total external torque on the body is zero, causing no change in angular momentum.</p> Signup and view all the answers

<p>Yes, a body can be in partial equilibrium, such as when it is in translational equilibrium but not in rotational equilibrium.</p> Signup and view all the answers

<p>The torque is $\tau = 2\hat{i} + 12\hat{j} + 10\hat{k}$.</p> Signup and view all the answers