Motion in A Pla...

The angle between \(\vec A= \hat i+\hat j\) and \(\vec B = \hat i - \hat j\) is

Which one of the following statements is true?

The component of vector r along X-axis will have maximum value if:

The horizontal range of a projectile fired at an angle of 15° is 50m. If it is fired with the same initial speed at an angle of 45°. its range will be:

In a two dimensional motion, instantaneous speed \(v_0\) is positive, constant. Then which of the following are necessarily true?

In a two-dimensional motion, instantaneous speed \(v_0\) is positive and constant. Then which of the following are necessarily true?

Three vectors \(\vec A\),\(\vec B\) and \(\vec C\) and add up to zero. Find which is false

(a) (\(\vec A\)x\(\vec B\)) x \(\vec C\) is not zero unless \(\vec B\) and \(\vec C\) are parallel

(b) (\(\vec A\)x\(\vec B\)).\(\vec C\) is not zero unless \(\vec B\),\(\vec C\) are parallel

(c) \(\vec A\),\(\vec B\),\(\vec C\) defined in a plane, (\(\vec A\)x\(\vec B\)) x \(\vec C\) is in that plane

(d) (\(\vec A\)x\(\vec B\)).\(\vec C\) = |\(\vec A\)||\(\vec B\)|\(\geq\)|\(\vec C\)| → \(C^2=A^2+B^2\)

It is found that \(|\vec A+\vec B|\) = \(|\vec A|\) this necessarily implies

Two particles are projected in air with speed \(v_0\) at angles \(\theta_1\) and \(\theta_2\) (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than of the second, then tick the right choices

(a) angle of projection: \(\theta_1>\theta_2\)

(b) time of flight: \(T_1>T_2\)

(c) horizontal range: \(R_1>R_2\)

(d) total energy: \(U_1<U_2\)

Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one(s).

(a) \(\vec \upsilon_{av}= {1\over2}[\vec \upsilon(t_1)+\vec \upsilon(t_2)]\)

(b) \(\vec \upsilon_{av}={\vec r(t_2)-\vec r(t_1)\over t_2-t_1}\)

(c) \(\vec r={1\over2}[\vec \upsilon(t_2)-\vec \upsilon(t_1)]\,÷\, (t_2-t_1)\)

(d) \(\vec a_{av}={\vec \upsilon(t_2)-\vec \upsilon(t_1)\over (t_2-t_1)}\)

For a particle performing uniform circular motion, choose the correct statement(s) from the following:

(a) Magnitude of particle velocity (speed) remains constant.

(b) Particle velocity remains directed perpendicular to radius vector.

(c) Direction of acceleration keeps changing as particle moves.

(d) Angular momentum is constant in magnitude but direction keeps changing.

For two vectors \(\vec A\) and \(\vec B\), \(|\vec A+\vec B|\) = \(|\vec A-\vec B|\) is always true when

(a) \(|\vec A|=|\vec B|\ne0\)

(b) \(\vec A\perp\vec B\)

(c) \(|\vec A|=|\vec B|\ne0\) and \(\vec A\) and \(\vec B\) are parallel or antiparallel

(d) When either \(|\vec A|\,or\ |\vec B|\) is zero