Questions
Which one of the following equations of motion represents simple harmonic motion?
- Acceleration =$-k _0x+k _1x^2$
- Acceleration =$-k(x+a)$
- Acceleration =$k(x+a)$
- Acceleration =$kx$
The mass of particle executing S.H.M is 1 gm.If its periodic time is $\pi $ seconds, the value of force constant is:-
- 4 dynes/cm
- 4 N/cm
- 4 N/m
- 4 dynes/m
A particle of mass 1kg is moving in a S.H.M with an amplitude of 0.02m and a frequency of 60Hz. The maximum force acting on the particle is :
- $2.88 \times 10^{3}$N
- $1.44 \times 10^{3}$N
- $5.67 \times 10^{3}$N
- $0.75 \times 10^{3}$N
In case of force oscillations of a body
- driving force is constant throughout.
- driving force is to be applied only momentarily.
- driving force has to be periodic and continuous.
- driving force is not required.
A student says that he had applied a force $F= -k\sqrt {x}$ on a particle and the particle moves in simple harmonic motion. He refuses to tell whether $k$ is a constant or not. Assume that he has worked only with positive $x$ and no other force acted on the particle.
- As $x$ increases $k$ increases
- As $x$ increases $k$ decreases
- As $x$ increases $k$ remains constant
- The motion cannot be simple harmonic
A body is executing SHM. If the force acting on the body is 6N when the displacement is 2 cm, then the force acting on the body when the displacement is 3 cm in newton is:
- $ 6 $ N
- $9$ N
- $4$ N
- $\sqrt{6} $ N
Restoring force in the SHM is
- conservative
- nonconservative
- frictional
- centripetal
In SHM, select the wrong statement, where ${F}$ is the force, ${a}$ is the acceleration and ${v}$ is the velocity of the particle in SHM.
- $\overset{\rightarrow}{F}\times \overset{\rightarrow}{v}$ is a null vector
- $|\overset{\rightarrow}{F}\times \overset{\rightarrow}{a}|=0$ (always)
- $\overset{\rightarrow}{F}\times \overset{\rightarrow}{a}< {0}$
- $\overset{\rightarrow}{a}.\overset{\rightarrow}{x}<0$
A coin is placed on a horizontal platform, which undergoes horizontal simple harmonic motion about a mean position $O$.The coin does not slip on the platform. The force of friction acting on the coin is $F$.
- $F$ is always directed towards $O$
- $F$ is directed towards $O$ when the coin is moving away from $O$, and away from $O$ when the coin moves towards $O$
- $F=0$ when the coin and platform come to rest momentarily at the extreme position of the harmonic motion.
- $F$ is maximum when the coin and platform come to rest momentarily at the extreme position of the harmonic motion.
The net external force acting on the disc when its centre of mass is at displacement $x$ with respect to its equilibrium position is:
- $-kx$
- $-2kx$
- $-\dfrac{2kx}{3}$
- $\dfrac{4kx}{3}$
A particle is in S.H.M of amplitude $ 2$ cm. At extreme position the force is $4$N. At the point mid-way between mean and extreme position, the force is :
- $1$ N
- $2$N
- $3$N
- $4$N
A 1 kg mass executes SHM with an amplitude 10 cm, it takes $2\pi$ seconds to go from one end to the other end. The magnitude of the force acting on it at any end is :
- 0.1 N
- 0.2 N
- 0.5 N
- 0.05 N
An elastic ball of density $d$ is released and it falls through a height $h$ before striking the surface of liquid of density $\rho(d < \rho)$. The motion of ball is:
- Periodic
- S.H.M.
- Circular
- Parabolic
A body of mass 1/4 kg is in S.H.M and its displacement is given by the relation $y= 0.05 sin(20t+\dfrac{\pi }{2})$ m. If $t$ is in seconds, the maximum force acting on the particle is:
- $5$ N
- $2.5$ N
- $10$ N
- $0.25$ N