Q. No.In Fig. 5.3, a body A of mass m slides on plane inclined at angle \(\theta_1\) to the horizontal and \(\mu_1\) is the coefficent of friction between A and the plane. A is connected by a light string passing over a frictionless pulley to another body B, also of mass m, sliding on a frictionless plane inclined at angle \(\theta_2\) to the horizontal. Which of the following statements are true?
a. A will never move up the plane.
b. A will just start moving up the plane when \(\mu=\frac{\sin \theta_2-\sin \theta_1}{\cos \theta_1} .\)
c. For A to move up the plane, \(\theta_2\) must always be greater than \(\theta_1\) .
d. B will always slide down with constant speed.
Choose the correct option:
1. (a), (d)
2. (a), (b), (d), (e)
3. (a), (b), (c)
4. (b), (c)
a. The impulse imparted to each ball is 0.25 kg m s–1 and the force on each ball is 250 N.
b. The impulse imparted to each ball is 0.25 kg m s–1 and the force exerted on each ball is 25 × 10–5 N.
c. The impulse imparted to each ball is 0.5 Ns.
d. The impulse and the force on each ball are equal in magnitude and opposite in direction.
Choose the correct option:
1. (a), (d)
2. (b), (c), (d)
3. (a), (b), (c)
4. (c), (d)
a. The force at t = (1/8) s on the particle is \(16 \pi^2~\text{Am}\)
b. The particle is acted upon by on impulse of magnitude \(4 \pi^2~\text{Am}\) at t = 0 s and t = (1/4) s.
c. The particle is not acted upon by any force.
d. The particle is not acted upon by a constant force.
e. There is no impulse acting on the particle.
Choose the correct option:
1. (a), (d)
2. (a), (b), (d)
3. (a), (b), (c)
4. (b), (c)
A body of mass \(10 ~\text{Kg}\) is acted upon by two perpendicular forces, \(6 ~\text{N}\) and \(8 ~\text{N}.\) The resultant acceleration of the body is:
| (a) | \(1~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{4}{3}\right ) \) w.r.t. \(6 ~\text{N}\) force. |
| (b) | \(0.2~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(8 ~\text{N}\) force. |
| (c) | \(1~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(8 ~\text{N}\) force. |
| (d) | \(0.2~\text{ms}^{-2}\) at an angle of \(\text {tan}^{-1} \left(\dfrac{3}{4}\right ) \) w.r.t. \(6 ~\text{N}\) force. |
Choose the correct option from the given ones:
| 1. | (a) and (c) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (a), (b) and (c) |
In figure a body \(A\) of mass \(m\) slides on a plane inclined at angle \(\left(\theta_{1}\right)\) to the horizontal and \(\mu\) is the coefficient of friction between \(A\) and the plane. \(A\) is connected by a light string passing over a frictionless pulley to another body \(B,\) also of mass \(m\), sliding on a frictionless plane inclined at an angle \(\left(\theta_{2}\right)\) to the horizontal.
| (a) | A will never move up the plane |
| (b) | A will just start moving up the plane when \(\mu = \dfrac{{\sin} \left(\theta\right)_{2} - {\sin} \left(\theta\right)_{1}}{{\cos} \left(\theta\right)_{1}}\) |
| (c) | For \(A\) to move up the plane, \(\left(\theta\right)_{2}\) must always be greater than \(\left(\theta\right)_{1}\) |
| (d) | \(B\) will always slide down with a constant speed |
Which of the following statement/s is/are true?
| 1. | (b, c) | 2. | (c, d) |
| 3. | (a, c) | 4. | (a, d) |
Mass \(m_{1}\) moves on a slope making an angle \(\theta\) with the horizontal and is attached to mass \(m_{2}\) by a string passing over a frictionless pulley as shown in the figure. The coefficient of friction between \(m_{1}\) and the sloping surface is \(\mu\).
| (a) | If \(m_{2} > m_{1} \text{sin} \theta \), the body will move up the plane. |
| (b) | If \(m_{2} > m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |
| (c) | If \(m_{2} < m_{1} (\text{sin} \theta +\mu \text{cos} \theta)\), the body will move up the plane. |
| (d) | If \(m_{2} < m_{1} (\text{sin} \theta -\mu \text{cos} \theta)\), the body will move down the plane. |
| 1. | (a), (d) | 2. | (a), (c) |
| 3. | (c), (d) | 4. | (b), (d) |
In the figure, the coefficient of friction between the floor and body \(B\) is \(0.1.\) The coefficient of friction between bodies \(B\) and \(A\) is \(0.2.\) A force \(F\) is applied as shown on \(B.\) The mass of \(A\) is \(m/2\) and of \(B\) is \(m.\)
| (a) | The bodies will move together if \(F = 0.25\text{mg}\) |
| (b) | The \(A\) will slip with \(B\) if \(F = 0.5\text{mg}\) |
| (c) | The bodies will move together if \(F = 0.5\text{mg}\) |
| (d) | The bodies will be at rest if \(F = 0.1\text{mg}\) |
| (e) | The maximum value of \(F\) for which the two bodies will move together is \(0.45\text{mg}\) |
Which of the following statement(s) is/are true?
1. (a), (b), (d), (e)
2. (a), (c), (d), (e)
3. (b), (c), (d)
4. (a), (b), (c)
The motion of a particle of mass \(m\) is given by \(x=0\) for \(t<0 ~\text s\), \(x(t)=A~\text {sin}~4\pi t\) for \(0<t<(1/4) \text s ~(A>0)\), and \(x=0\) for \(t>(1/4) ~\text s\). Then:
| (a) | The force at \(t=(1/8) ~\text s \) on the particle is \(-16 \pi^2\text{Am}\) |
| (b) | The particle is acted upon by an impulse of magnitude \(4 \pi^2 \text{Am}\) at \(t=0 ~\text s\) and \(t=(1/4) ~\text s\) |
| (c) | The particle is not acted upon by any force |
| (d) | The particle is not acted upon by a constant force |
| (e) | There is no impulse acting on the particle |
Which of the following statement/s is/are true?
| 1. | (a, c, d, e) | 2. | (a, c) |
| 3. | (b, c, d) | 4. | (a, b, d) |
A car of mass \(m\) starts from rest and acquires a velocity along the east, \(v=v\mathrm{\hat{i}}(v>0)\) in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is:
| 1. | \(mv/2 \) eastward and is exerted by the car engine. |
| 2. | \(mv/2\) eastward and is due to the friction on the tires exerted by the road. |
| 3. | more than \(mv/2\) eastward exerted due to the engine and overcomes the friction of the road. |
| 4. | \(mv/2\) exerted by the engine. |
A body with a mass of \(5\) kg is acted upon by a force \(\vec{F}=( -3\hat{i} +4\hat{j})\) N. If its initial velocity at \(t=0\) is \(\vec{v}= ( 6\hat{i} -12\hat{j} )\) m/s, the time at which it will just have a velocity along the \(y\)-axis is:
1. never
2. \(10\) s
3. \(2\) s
4. \(15\) s
© 2026 GoodEd Technologies Pvt. Ltd.